Mathematical Methods in the Applied Sciences最新文献

{"title":"Mathematical modeling of containing the spread of heroin addiction via awareness program","authors":"Salih Djilali, Amine Loumi, Soufiane Bentout, Ghilmana Sarmad, Abdessamad Tridane","doi":"10.1002/mma.10544","DOIUrl":"https://doi.org/10.1002/mma.10544","url":null,"abstract":"<p>As many countries are hit by the social economic impact of heroin addiction, there is an urgent need to have an effective awareness program that focuses on educating the population on the danger of heroin addiction and helping the heroin-users quit. This paper aims to study the effect of the awareness program on the spread of heroin dependence using a mathematical model with distributed delay. First, we show the existence threshold parameter \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathfrak{R}}_0 $$</annotation>\u0000 </semantics></math>, which we call the basic reproduction number of the spread of heroin use. We prove, via the Lyapunov direct method, that the drug-free equilibrium is globally asymptotically stable if \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo><</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ {mathfrak{R}}_0<1 $$</annotation>\u0000 </semantics></math>. If \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>></mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ {mathfrak{R}}_0>1 $$</annotation>\u0000 </semantics></math>, the drug dependence persists, and the drug equilibrium is globally asymptotically stable. We give three possible scenarios to find the optimal awareness program strategy that puts the heroin epidemic under control. These scenarios take into consideration the reachability of the population, the immunity against heroin addiction, and the effectiveness of the program to contain the use of heroin in the population and bring \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathfrak{R}}","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4244-4261"},"PeriodicalIF":2.1,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10544","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On proportional hybrid operators in the discrete setting","authors":"Carlos Lizama,&nbsp;Marina Murillo-Arcila","doi":"10.1002/mma.10551","DOIUrl":"https://doi.org/10.1002/mma.10551","url":null,"abstract":"<p>In this article, we introduce a new nonlocal operator \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}&amp;amp;#x00026;#x0005E;{alpha } $$</annotation>\u0000 </semantics></math> defined as a linear combination of the discrete fractional Caputo operator and the fractional sum operator. A new dual operator \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {R}&amp;amp;#x00026;#x0005E;{alpha } $$</annotation>\u0000 </semantics></math> is also introduced by replacing the discrete fractional Caputo operator with the discrete fractional Riemann–Liouville operator. It is shown that it corresponds to a natural discretization of a proportional hybrid operator defined by the Riemann–Liouville operator instead of Caputo hybrid operator. We then analyze the most important properties of these operators, such as their inverse operator and the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <annotation>$$ Z $$</annotation>\u0000 </semantics></math>-transform, among others. As an application, we solve difference equations equipped with these operators and obtain explicit solutions for them in terms of trivariate Mittag-Leffler sequences.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4344-4364"},"PeriodicalIF":2.1,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10551","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak and strong solutions for a fluid-poroelastic-structure interaction via a semigroup approach","authors":"George Avalos,&nbsp;Elena Gurvich,&nbsp;Justin T. Webster","doi":"10.1002/mma.10533","DOIUrl":"https://doi.org/10.1002/mma.10533","url":null,"abstract":"<p>A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow is considered in 3D. Across the flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. In the inertial, linear, and non-degenerate case, the hyperbolic-parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes-Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non-standard maximality argument. The latter employs a mixed-variational formulation in order to invoke the Babuška-Brezzi theorem. The Lumer-Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot-Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4057-4089"},"PeriodicalIF":2.1,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Determination of two unknown functions of different variables in a time-fractional differential equation","authors":"Mokhtar Kirane,&nbsp;Andriy Lopushansky,&nbsp;Halyna Lopushanska","doi":"10.1002/mma.10539","DOIUrl":"https://doi.org/10.1002/mma.10539","url":null,"abstract":"<p>We study the inverse problem for a differential equation of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 <annotation>$$ 2b $$</annotation>\u0000 </semantics></math>-order with the Caputo fractional derivative over time and Schwartz-type distribution in its right-hand side. The generalized solution of the Cauchy problem for such an equation, space-dependent part of a source, and a time-dependent reaction coefficient in the equation are unknown. We find sufficient conditions for unique local in time solvability of the inverse problem under time- and space-integral overdetermination conditions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4185-4194"},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Zero-Hopf bifurcation in a family of tritrophic food chain model with Holling III–III functional response","authors":"Víctor Castellanos,&nbsp;Jaume Llibre","doi":"10.1002/mma.10494","DOIUrl":"https://doi.org/10.1002/mma.10494","url":null,"abstract":"<p>In this paper, we apply the second-order averaging theory for obtaining an explicit expression of the small amplitude periodic solution that bifurcates from a zero-Hopf equilibrium point of a tritrophic food chain model. This model considers logistic growth rate for the lowest trophic level, Holling functional responses type III for the middle and for the highest level. We first prove that this model has a zero-Hopf equilibrium point, after we show that from this equilibrium bifurcates a small limit cycle, and finally, we provide the explicit expression of the first two terms in the power series of this limit cycle. These differential systems for which the equilibrium point is non hyperbolic are not easy to study, in particular, if the equilibrium is zero-Hopf. As far as we know, this is the first time that the averaging theory has been used to exhibit the first and second terms of the power series expansion of the analytical expression of a limit cycle that bifurcates from a zero-Hopf equilibrium in the food chain models.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3434-3447"},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The positive solutions for a class of Kirchhoff-type problems with critical Sobolev exponents on a bounded domain","authors":"Xiaoxue Zhu,&nbsp;Haining Fan","doi":"10.1002/mma.10535","DOIUrl":"https://doi.org/10.1002/mma.10535","url":null,"abstract":"<p>We study the positive solutions for a class of Kirchhoff-type problems involving the nonlinearity \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mi>g</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>4</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ lambda f(x){u}&amp;amp;#x00026;#x0005E;{p-1}&amp;amp;#x00026;#x0002B;g(x){u}&amp;amp;#x00026;#x0005E;5left(2&amp;amp;#x0003C;p&amp;amp;#x0003C;4right) $$</annotation>\u0000 </semantics></math> on a bounded domain. The major difficulty of such problems is the nonlinearity does not satisfy the Ambrosetti–Rabinowitz condition; especially, we cannot use Pohozaev's identity directly since our domain is bounded and the weight potentials are not \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}&amp;amp;#x00026;#x0005E;1 $$</annotation>\u0000 </semantics></math>-smoothness. Another difficulty is caused by the absence of compactness as the appearance of the critical Sobolev growth. In this work, we shall combine the Nehari manifold and some novel analytical skills to overcome the above difficulties and then obtain some existence results. Furthermore, we show some asymptotic behaviors of the solutions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4090-4116"},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatiotemporal fluctuation induces Turing pattern formation in the chemical Brusselator","authors":"Quan Yuan,&nbsp;Sizhe Wang,&nbsp;Ting Lai,&nbsp;Haohua Wang","doi":"10.1002/mma.10482","DOIUrl":"https://doi.org/10.1002/mma.10482","url":null,"abstract":"<p>Chemical reactions are embedded in spatiotemporal fluctuations instead of a constant environment. Here, we aimed to assess reaction–diffusion (RD) with dichotomous noise-controlling system parameters in the Brusselator and examine the effect of these fluctuations on the dynamic behavior of chemical reactions. By performing a multiscale perturbation analysis, we demonstrated that the correlated noise can broaden the Turing region even if molecular memory (autocorrelation time) exists. However, for small noise, short-term memory promotes Turing instability. The instability of the Brusselator is determined by the noise strength, which belongs to the optimal region if the diffusion coefficient is fixed. Turing pattern selection and stability are also governed by the dynamic character of the amplitude equation, and the entire Turing instability region shifts to the right in the phase space with noise perturbation. Finally, numerical simulations validate the theoretical derivation that correlated noise can amplify Turing pattern formation to maintain distinct patterns.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3233-3252"},"PeriodicalIF":2.1,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the impact of screening awareness and vaccination on human papilloma virus transmission","authors":"Ling Xue,&nbsp;Shang Zhou,&nbsp;Yuxin Zhang","doi":"10.1002/mma.10529","DOIUrl":"https://doi.org/10.1002/mma.10529","url":null,"abstract":"&lt;p&gt;In this work, a two-sex deterministic model for human papillomavirus (HPV) is developed to assess the impact of screening awareness and vaccination on the transmission dynamics. We provide a detailed analysis of the HPV model and established results for boundedness of the solutions and existence of a positively invariant and attracting set. The basic reproduction number \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is characterized, and it is shown that the disease-free equilibrium is locally asymptotically stable if \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0&amp;amp;lt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the system is uniformly persistent if \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0&amp;amp;gt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Sensitivity analysis of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; reveals that HPV vaccination can mitigate HPV transmission, and HPV vaccination along with screening can further reduce the spread of HPV infection. Numerical simulations showed that the public awareness of screening after being vaccinated is contributing to reduce the spread of epidemic, and the role of screening awareness in controlling the disease was significantly greater among men than women. Besides, the numerical simulations reveal that increasing vaccination rates for male is effective in controlling HPV transmission. Hence, it is necessary to enhance the screening for men. Moreover, increasing vaccination rates is more effective than increasing screeni","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3979-3997"},"PeriodicalIF":2.1,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weakly coupled systems of semilinear σ-evolution equations with friction and visco-elastic type damping","authors":"Mohamed Kainane Mezadek,&nbsp;Michael Reissig","doi":"10.1002/mma.10473","DOIUrl":"https://doi.org/10.1002/mma.10473","url":null,"abstract":"&lt;p&gt;In the present paper, we are interested to study global (in time) existence of small data Sobolev solutions to the Cauchy problem for a weakly coupled system of two semilinear \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {sigma}_k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-evolution equations with friction and visco-elastic type damping, where \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {sigma}_kgeqslant 1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1,2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ k&amp;amp;amp;#x0003D;1,2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We study model (1.1) (see below) in several cases with respect to the regularity for the data: First, we assume data \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3022-3063"},"PeriodicalIF":2.1,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10473","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow dynamics over cylinder in two-dimensional benchmark problem: A finite element approximation","authors":"Sadaf Nasreen,&nbsp;Taj Munir,&nbsp;Saif Ullah,&nbsp;Hussan Zeb,&nbsp;N. Ameer Ahammad,&nbsp;Mohamed Abdelghany Elkotb","doi":"10.1002/mma.10527","DOIUrl":"https://doi.org/10.1002/mma.10527","url":null,"abstract":"<p>This research investigates 2D benchmark flow around a circular cylinder, utilizing the incompressible Navier–Stokes equations alongside the continuity and energy equations. The numerical solution is achieved through finite element discretization for space variable, combined with a second-order Crank–Nicolson scheme for time integration. The computational results are derived using the FEATFLOW finite element based library package. Our study focuses on the dimensionless form of the flow equations and examines three key dimensionless parameters: drag, lift, and pressure drop. Upon applying finite element method (FEM) discretization, the system is converted into a set of linear or nonlinear ordinary differential equations or algebraic equations for steady-state scenarios. We then apply the Newton–Raphson method as the outer nonlinear solver, and the multigrid method for efficiently resolving the linear subproblems. To ensure numerical accuracy, we evaluated the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {L}_2 $$</annotation>\u0000 </semantics></math> and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}&amp;amp;amp;#x0005E;1 $$</annotation>\u0000 </semantics></math> errors, confirming that the experimental order of convergence matches the theoretical predictions. Flow profiles were both graphically represented and tabulated, offering a detailed understanding of the simulation results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3956-3965"},"PeriodicalIF":2.1,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}