Nonlinear Analysis-Real World Applications最新文献

{"title":"Time geodesics on a slippery cross slope under gravitational wind","authors":"Nicoleta Aldea ,&nbsp;Piotr Kopacz","doi":"10.1016/j.nonrwa.2024.104177","DOIUrl":"10.1016/j.nonrwa.2024.104177","url":null,"abstract":"<div><p>In this work, we pose and solve the time-optimal navigation problem considered on a slippery mountain slope modeled by a Riemannian manifold of an arbitrary dimension, under the action of a cross gravitational wind. The impact of both lateral and longitudinal components of gravitational wind on the time geodesics is discussed. The varying along-gravity effect depends on traction in the presented model, whereas the cross-gravity additive is taken entirely in the equations of motion, for any direction and gravity force. We obtain the conditions for strong convexity and the purely geometric solution to the problem is given by a new Finsler metric, which belongs to the type of general <span><math><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></math></span>-metrics. The proposed model enables us to create a direct link between the Zermelo navigation problem and the slope-of-a-mountain problem under the action of a cross gravitational wind. Moreover, the behavior of the Finslerian indicatrices and time-minimizing trajectories in relation to the traction coefficient and gravitational wind force are explained and illustrated by a few examples in dimension two. This also compares the corresponding solutions on the slippery slopes under various cross- and along-gravity effects, including the classical Matsumoto’s slope-of-a-mountain problem and Zermelo’s navigation.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141960673","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 discontinuous planar piecewise linear systems with two improper nodes have at most one limit cycle","authors":"Lu Chen,&nbsp;Changjian Liu","doi":"10.1016/j.nonrwa.2024.104180","DOIUrl":"10.1016/j.nonrwa.2024.104180","url":null,"abstract":"<div><p>The existence and number of limit cycles of planar piecewise linear systems with two improper nodes are studied. By constructing the Poincaré half maps and the successor function, we prove that such systems have at most one limit cycle, and when the limit cycle exists, it must be hyperbolic. Furthermore, we explicitly give the parameter regions where the limit cycle exists.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141637930","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":"Dynamical analysis of SARS-CoV-2-Dengue co-infection mathematical model with optimum control and sensitivity analyses","authors":"R. Prem Kumar ,&nbsp;G.S. Mahapatra ,&nbsp;P.K. Santra","doi":"10.1016/j.nonrwa.2024.104175","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104175","url":null,"abstract":"<div><p>This study develops an epidemic model to analyze the dynamics of SARS-CoV-2 and dengue coinfection in a population. The population is divided into sixteen compartments for humans and three for vectors. The model’s validity is ensured by maintaining bounded and non-negative solutions. The Basic Reproduction Number (BRN) is calculated for each sub-model to assess stability at equilibrium points. Sensitivity analysis identifies key parameters influencing the model. The complete coinfection model is analyzed to identify equilibrium points and evaluate stability conditions. The reciprocal influence of SARS-CoV-2 and dengue diseases is examined. An optimal control problem is formulated, incorporating six strategies: COVID-19 protection, mosquito bite prevention, treatment for COVID-19 and dengue, mosquito control, and coinfection treatment. Numerical simulations validate the effectiveness of these control strategies for the coinfection model and its sub-models.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141607111","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":"Boundary optimal control problem of semi-linear Kirchhoff plate equation","authors":"Abdelhak Bouhamed ,&nbsp;Abella Elkabouss ,&nbsp;Pitágoras P. de Carvalho ,&nbsp;Hassane Bouzahir","doi":"10.1016/j.nonrwa.2024.104146","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104146","url":null,"abstract":"<div><p>This paper examines a nonlinear Kirchhoff plate equation, where the control acts in bilinear form within the boundary of the mentioned equation. The objective is to construct a distributed control to guide such a system from the initial state to the desired state in the final time, while minimizing a quadratic functional cost defined as the sum of the norm difference between the aforementioned state and a desired equation with an energy term. We show how to approximate the solution of the nonlinear Kirchhoff plate equation to a desired objective, indicating the existence of optimal control in specific cases. and deriving the optimally conditions for a closed convex set. Moreover, it is shown that sufficient conditions ensures the uniqueness of control optimal. Furthermore, we provide a concise numerical methodology that involves the integration of finite element and finite difference discretization methods. The approach incorporates Newton’s linearization method to assess the computational performance of the controlled problem, using the Freefem++ software.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141593949","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":"Global classical solutions to a chemotaxis consumption model involving singularly signal-dependent motility and logistic source","authors":"Liangchen Wang,&nbsp;Rui Huang","doi":"10.1016/j.nonrwa.2024.104174","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104174","url":null,"abstract":"<div><p>This work considers the Keller–Segel consumption system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mrow><mo>(</mo><mi>u</mi><msup><mrow><mi>v</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>u</mi><mo>−</mo><mi>b</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>γ</mi></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>under homogeneous Neumann boundary conditions in a smooth bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, where the parameters <span><math><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>γ</mi><mo>≥</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, the initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mn>0</mn><mrow><mo>(</mo><mo>⁄</mo><mo>≡</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow></math></span> in <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> with <span><span><span><math><mrow><msub><mrow><mo>‖</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub><mo>&lt;</mo><mo>exp</mo><mfenced><mrow><mfrac><mrow><mo>ln</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mi>α</mi></mrow><mrow><mi>α</mi></mrow></mfrac><mi>⋅</mi><mfrac><mrow><mn>8</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></mrow></mrow><mrow><mi>α</mi></mrow></mfrac></mrow></mfenced><mo>.</mo></mrow></","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141593950","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":"Bifurcation of limit cycles from a periodic annulus formed by a center and two saddles in piecewise linear differential system with three zones","authors":"Claudio Pessoa ,&nbsp;Ronisio Ribeiro","doi":"10.1016/j.nonrwa.2024.104171","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104171","url":null,"abstract":"<div><p>In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the linear differential systems that define the piecewise one have a center and two saddles. That is, the linear differential system in the region between the two parallel lines (called of central subsystem) has a center and the others subsystems have saddles. We prove that if the central subsystem has a real or a boundary center, then at least six limit cycles can bifurcate from the periodic annulus by linear perturbations. Four passing through the three zones and two passing through two zones. Now, if the central subsystem has a virtual center, then at leas four limit cycles can bifurcate from the periodic annulus by linear perturbations, three passing through the three zones and one passing through two zones. For this, we obtain a normal form for these piecewise Hamiltonian systems and study the number of zeros of its Melnikov functions defined in two and three zones.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481796","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":"Convergence rate toward shock wave under periodic perturbation for generalized Korteweg–de Vries–Burgers equation","authors":"Lin Chang","doi":"10.1016/j.nonrwa.2024.104170","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104170","url":null,"abstract":"<div><p>In this paper, a viscous shock wave under space-periodic perturbation of generalized Korteweg–de Vries–Burgers equation is investigated. It is shown that if the initial periodic perturbation around the viscous shock wave is small, then the solution time asymptotically tends to a viscous shock wave with a shift partially determined by the periodic oscillations. Moreover the exponential time decay rate toward the viscous shock wave is also obtained for some certain perturbations.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141482154","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":"Global existence of solutions to some degenerate chemotaxis systems with superlinear growth in cross-diffusion rates and logistic sources","authors":"Minh Le","doi":"10.1016/j.nonrwa.2024.104168","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104168","url":null,"abstract":"<div><p>The objective is to investigate the global existence of solutions for degenerate chemotaxis systems with logistic sources in a two-dimensional domain. It is demonstrated that the inclusion of logistic sources can exclude the occurrence of blow-up solutions, even in the presence of superlinear growth in the cross-diffusion rate. Our proof relies on the application of elliptic and parabolic regularity in Orlicz spaces and variational approach.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481795","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 local well-posedness of the coupled Ostrovsky system with low regularity","authors":"Ting Luo,&nbsp;Weifeng Zhang","doi":"10.1016/j.nonrwa.2024.104166","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104166","url":null,"abstract":"<div><p>In this paper, the Cauchy problem for the coupled Ostrovsky equations with an initial value in the Sobolev spaces <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> of lower order <span><math><mi>s</mi></math></span> is considered. With the bilinear estimate, it is proved that the initial value problem is locally well-posed in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mo>&gt;</mo><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></span> by using Bourgain spaces. Moreover, if <span><math><mrow><mi>s</mi><mo>&lt;</mo><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></span>, it is demonstrated that one of the nonlinear iteration from the initial data to the putative solutions is discontinuous with an argument on the high-to-low frequency. In this sense, it is then concluded that the coupled Ostrovsky equations is ill-posed in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mo>&lt;</mo><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></span>.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481791","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":"Solutions of impulsive p(x,t)-parabolic equations with an infinitesimal initial layer","authors":"Stanislav Antontsev ,&nbsp;Ivan Kuznetsov ,&nbsp;Sergey Sazhenkov ,&nbsp;Sergey Shmarev","doi":"10.1016/j.nonrwa.2024.104162","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104162","url":null,"abstract":"<div><p>We study the multi-dimensional Cauchy–Dirichlet problem for the <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>-parabolic equation with a regular nonlinear minor term, which models a non-instantaneous but very rapid absorption with the <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>-growth. The minor term depends on a positive integer parameter <span><math><mi>n</mi></math></span> and, as <span><math><mrow><mi>n</mi><mo>→</mo><mo>+</mo><mi>∞</mi></mrow></math></span>, converges weakly<span><math><msup><mrow></mrow><mrow><mo>⋆</mo></mrow></msup></math></span> to the expression incorporating the Dirac delta function, which, in turn, models an instant absorption at the initial moment. We prove that an infinitesimal initial layer, associated with the Dirac delta function, is formed as <span><math><mrow><mi>n</mi><mo>→</mo><mo>+</mo><mi>∞</mi></mrow></math></span>, and that the family of regular weak solutions of the original problem converges to the so-called ‘strong-weak’ solution of a two-scale microscopic–macroscopic model. Furthermore, the equation of the microstructure can be integrated explicitly, which leads in a number of cases to the purely macroscopic formulation for the <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>-parabolic equation provided with the corrected initial data.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481794","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}