Mathematical Methods in the Applied Sciences最新文献

{"title":"CMMSE: New Properties of Auto-Wave Solutions in Activator-Inhibitor Reaction-Diffusion Systems With Fractional Derivatives","authors":"Bohdan Datsko,&nbsp;Vasyl Gafiychuk","doi":"10.1002/mma.10672","DOIUrl":"https://doi.org/10.1002/mma.10672","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we analyze new properties of auto-wave solutions in fractional reaction-diffusion systems. These new properties arise due to a change in fractional derivative order and do not occur in systems with classical derivatives. It is shown that the stability of steady-state solutions and their evolution are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative order. It is also demonstrated that the basic properties of auto-wave solutions in fractional-order systems can essentially differ from those in standard systems. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol–FitzHugh–Nagumo mathematical model. A common picture of possible instabilities and auto-wave solutions in time-fractional two-component activator-inhibitor systems is presented.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6292-6302"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622342","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":"Local Well-Posedness of Kolmogorov'S Two-Equation Model of Turbulence in Fractional Sobolev Spaces","authors":"Przemysław Kosewski","doi":"10.1002/mma.10643","DOIUrl":"https://doi.org/10.1002/mma.10643","url":null,"abstract":"<div>\u0000 \u0000 <p>We study Kolmogorov's two-equation model of turbulence on \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$$ d $$</annotation>\u0000 </semantics></math>-dimensional torus. First, the local existence of the solution with the initial data from non-homogeneous fractional Sobolev spaces (Bessel potential spaces) \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}^s $$</annotation>\u0000 </semantics></math> with \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>&gt;</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$$ s&gt;frac{d}{2} $$</annotation>\u0000 </semantics></math> is proven using energy methods. Next, we show that solutions are unique in the class of solutions guaranteed by the local existence theorem.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5872-5895"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595695","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":"Seasonal Stochasticity Drives Phytoplankton–Zooplankton Dynamics","authors":"Nazmul Sk,&nbsp;Subarna Roy,&nbsp;Pankaj Kumar Tiwari","doi":"10.1002/mma.10651","DOIUrl":"https://doi.org/10.1002/mma.10651","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we examine a deterministic model incorporating refuge, additional food sources, and toxins. The existence and stability of positive equilibria and the bifurcation analyses are discussed. Our numerical outcomes entail that increased zooplankton growth due to additional food leads to the disappearance of phytoplankton species, while a significant drop in nutrient levels results in zooplankton extinction within the ecosystem. Notably, the refuge by phytoplankton has a tendency to terminate the persistent oscillations and stabilize the system. As seasonal stochasticity significantly influences the dynamics of planktonic system, so we introduce seasonality into environmental noise and certain model parameters. In this case, we analyze both the regularity and the dichotomy between persistence and extinction. The numerical evidences demonstrate periodic solutions, strong/weak persistence, and plankton extinctions resulting from stochasticity and/or seasonality. Furthermore, the seasonally forced noise, intriguingly, has the capacity to exert control over hyperchaos, yielding a distinctive pattern in plankton populations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5998-6018"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595693","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":"Approximation Properties of \u0000(λ,μ)-Bernstein-Durrmeyer Operators","authors":"Qing-Bo Cai,&nbsp;Guorong Zhou","doi":"10.1002/mma.10647","DOIUrl":"https://doi.org/10.1002/mma.10647","url":null,"abstract":"<div>\u0000 \u0000 <p>In this manuscript, a new kind of (\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation>$$ lambda, kern0.3em mu $$</annotation>\u0000 </semantics></math>)-Bernstein-Durrmeyer operators is introduced. A Korovkin-type approximation theorem is obtained, the rate of convergence is investigated by using the modulus of smoothness, Lipschitz continuous function, and Steklov mean, a Voronovskaja asymptotic formula is established, and graphical representations and numerical examples are also presented to compare the newly defined ones with other forms.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5946-5953"},"PeriodicalIF":2.1,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595643","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":"Existence and Uniqueness Results for Fractional Differential Equations With Nonlocal Conditions in \u0000Lp Spaces","authors":"Kiran Kumar Saha,&nbsp;N. Sukavanam","doi":"10.1002/mma.10633","DOIUrl":"https://doi.org/10.1002/mma.10633","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper deals with nonlocal initial value problems (IVPs) for modified Caputo fractional differential equations (FDEs) of order \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 <annotation>$$ alpha $$</annotation>\u0000 </semantics></math> \u0000 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>α</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left(0&lt;alpha &lt;1right) $$</annotation>\u0000 </semantics></math>. The novelty of this work is that the nonlinearity \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 <annotation>$$ f $$</annotation>\u0000 </semantics></math> is considered in \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^p $$</annotation>\u0000 </semantics></math> spaces, where \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$$ 1le p&lt;infty $$</annotation>\u0000 </semantics></math>, instead of the conventional space of continuous functions. In each scenario, we meticulously derive the equivalences between the FDEs and the corresponding integral equations in the spaces of interest. Several new existence and uniqueness results based on the Banach contraction principle are established, imposing weaker assumptions on the data as much as possible. To exemplify our main results, we present three constructive examples, together with their corresponding unique solution trajectories.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5745-5754"},"PeriodicalIF":2.1,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595472","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":"Local Well-Posedness to the Magneto-Micropolar Boundary Layer Equations in Gevrey Space","authors":"Zhong Tan,&nbsp;Mingxue Zhang","doi":"10.1002/mma.10637","DOIUrl":"https://doi.org/10.1002/mma.10637","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the boundary layer equations for two-dimensional magneto-micropolar boundary layer system and establish the existence and uniqueness of solutions in the Gevrey function space without any structural assumption, with Gevrey index \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$$ sigma in left(1,frac{3}{2}right] $$</annotation>\u0000 </semantics></math>. Inspired by the abstract Cauchy-Kovalevskaya theorem, our proof is based on a new cancellation mechanism in the system to overcome the difficulties caused by the loss of derivatives. Our results improve the classical local well-posedness results presented in a previous study, specifically for cases where the initial data are analytic in the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <annotation>$$ x $$</annotation>\u0000 </semantics></math>-variable.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5790-5802"},"PeriodicalIF":2.1,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595471","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":"Spectrum-Related Theories in the Framework of Quadratic Phase Fourier Transform","authors":"Sarga Varghese,&nbsp;Manab Kundu","doi":"10.1002/mma.10642","DOIUrl":"https://doi.org/10.1002/mma.10642","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, new type of convolution and correlation theorems associated with quadratic phase Fourier transform (QPFT) are studied. Applications of that in multiplicative filter design, which may be useful in optics and signal processing to recover the signals, are also discussed. Besides that, the real Paley–Wiener (PW) and Boas theorem for QPFT are proved, which analyses the characteristics of the signals associated with QPFT in the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^2 $$</annotation>\u0000 </semantics></math> domain.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5863-5871"},"PeriodicalIF":2.1,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595478","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":"CMMSE: Solutions in a Broad Sense to the Boundary Value Problem for First-Order Partial Differential Systems","authors":"Altynshash Bekbauova","doi":"10.1002/mma.10669","DOIUrl":"https://doi.org/10.1002/mma.10669","url":null,"abstract":"<div>\u0000 \u0000 <p>This article examines the initial-boundary value problem for a system of first-order partial differential equations. Issues of existence and uniqueness of the solution in a broad sense are considered, while taking into account both periodic and multipoint conditions. The definition of a solution in a broad sense is introduced; the initial problem is reduced to the initial-boundary value problem for ordinary differential equations. The two-point boundary value problem for ordinary differential equations systems is studied by the Dzhumabaev method (parameterization method), which allows us to move on to the equivalent multipoint boundary value problem with functional parameters. An algorithm to find an approximate solution to the problem in a broad sense has been developed.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6263-6268"},"PeriodicalIF":2.1,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622488","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":"A Posteriori Error Estimates for Exponential Midpoint Integrator Finite Element Method for Parabolic Equations","authors":"Xianfa Hu,&nbsp;Wansheng Wang,&nbsp;Yonglei Fang","doi":"10.1002/mma.10641","DOIUrl":"https://doi.org/10.1002/mma.10641","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, a posteriori error estimates for the fully discrete approximation for linear and semilinear parabolic equations are established. The exponential midpoint method is used for the temporal discretization, and the spatial discretization takes the standard linear elements. By introducing a continuous piecewise quadratic reconstruction, the error of the temporal discretization is derived. The error of the spatial discretization is evaluated by the interpolation estimates. Using the energy technique, we derive residual-based a posteriori lower and upper bounds for the fully discrete approximation. Our theoretical results are supported by extensive numerical experiments.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5849-5862"},"PeriodicalIF":2.1,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595479","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":"Homogenization for a Class Stochastic Partial Differential Equations With Nonperiodic Coefficients","authors":"Dong Su,&nbsp;Xuan Yang","doi":"10.1002/mma.10623","DOIUrl":"https://doi.org/10.1002/mma.10623","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper deals with homogenization for a class stochastic partial differential equations with nonperiodic coefficients. By means of the stochastic two-scale convergence approach, the solution of a class stochastic partial differential equations with nonperiodic coefficients (microscopic model) is shown to converge in distribution to the solution of effective equation (macroscopic model).</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5611-5618"},"PeriodicalIF":2.1,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595642","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}