Nonlinear Analysis-Real World Applications最新文献

{"title":"Large relaxation oscillation in slow–fast excitable Brusselator oscillator","authors":"Liyan Zhong ,&nbsp;Jianhe Shen","doi":"10.1016/j.nonrwa.2024.104138","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104138","url":null,"abstract":"<div><p>In general, critical manifold loses normal hyperbolicity at folded, transcritical and pitchfork singularities. There is another situation where normal hyperbolicity of critical manifold fails, namely, the alignment of the tangent and normal bundles at the unbounded part of critical manifold. In this case, how to reveal the attracting or repelling natures of unbounded critical manifold is essential to detect the birth of relaxation oscillations. In this article, after the compactification of the unbounded critical curve and then blowing-up the resulting degenerate line, we find that return mechanism exists at the <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>ɛ</mi><mo>)</mo></mrow></mrow></math></span>-region of the critical curve in a slow–fast excitable Brusselator oscillator. By so doing the birth of relaxation oscillation near the unbounded critical curve in this model is demonstrated. In addition, we reveal the continuation process from Hopf small-amplitude cycle to large relaxation oscillation of size <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>ɛ</mi><mo>)</mo></mrow></mrow></math></span> in the blown-up space. This may be the counterpart of canard explosion in unbounded situation. All the theoretical predictions are verified by numerical simulations.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141072615","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":"On a fourth order equation describing single-component film models","authors":"Martina Magliocca","doi":"10.1016/j.nonrwa.2024.104137","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104137","url":null,"abstract":"<div><p>We study existence results for a fourth order problem describing single-component film models assuming initial data in Wiener spaces.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824000774/pdfft?md5=fa090be4457e4225e16eb90fa56fba0e&pid=1-s2.0-S1468121824000774-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951343","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":"Uniform-in-time boundedness in a class of local and nonlocal nonlinear attraction–repulsion chemotaxis models with logistics","authors":"Alessandro Columbu,&nbsp;Rafael Díaz Fuentes,&nbsp;Silvia Frassu","doi":"10.1016/j.nonrwa.2024.104135","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104135","url":null,"abstract":"<div><p>The following fully nonlinear attraction–repulsion and zero-flux chemotaxis model is studied: <span><span><span>(<span><math><mo>♢</mo></math></span>)</span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><msup><mrow><mrow><mo>(</mo><mi>u</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn></mrow></msup><mo>∇</mo><mi>u</mi><mo>−</mo><mi>χ</mi><mi>u</mi><msup><mrow><mrow><mo>(</mo><mi>u</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>1</mn></mrow></msup><mo>∇</mo><mi>v</mi></mrow></mfenced><mspace></mspace></mtd></mtr><mtr><mtd><mfenced><mrow><mspace></mspace><mo>+</mo><mi>ξ</mi><mi>u</mi><msup><mrow><mrow><mo>(</mo><mi>u</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>−</mo><mn>1</mn></mrow></msup><mo>∇</mo><mi>w</mi></mrow></mfenced><mo>+</mo><mi>λ</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>r</mi></mrow></msup><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><mi>τ</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>ϕ</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><mi>τ</mi><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>ψ</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>)</mo></mrow><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>Herein, <span><math><mi>Ω</mi></math></span> is a bounded and smooth domain of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, for <span><math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math></span>, <span><math><mrow><mi>χ</mi><mo>,</mo><mi>ξ</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>r</mi></mrow></math></span> proper positive numbers, <span><math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824000750/pdfft?md5=7ea2ce86ba1b3e1921a481bb478cddb6&pid=1-s2.0-S1468121824000750-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951342","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":"Persistence of a competition model of plankton allelopathy in time–space periodic environment","authors":"Li-Jun Du,&nbsp;Li Zhang,&nbsp;Qian Cao","doi":"10.1016/j.nonrwa.2024.104136","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104136","url":null,"abstract":"<div><p>This work is devoted to the study of a competition model of plankton allelopathy imposed in time-space periodic environment. We prove that the system admits positive periodic solutions under certain conditions. We further obtain some sufficient conditions for the uniqueness and global stability of the positive periodic solution, which shows that the model is persistent. The main tools for our arguments are comparison theorems based on the maximum principle, sub- and supersolutions method, and an iteration method, which also permit the treatment of some more general reaction–diffusion models in periodic environment.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140914268","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":"Minimization principle for hemivariational–variational inequality driven by uniformly monotone operators with application to problems in contact mechanics","authors":"Michał Bełdziński,&nbsp;Marek Galewski,&nbsp;Filip Pietrusiak","doi":"10.1016/j.nonrwa.2024.104134","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104134","url":null,"abstract":"<div><p>In this paper, we consider hemivariational–variational inequalities driven by uniformly monotone or <span><math><mi>d</mi></math></span>-monotone operators in Banach spaces. We establish related minimization principles leading to the existence and uniqueness of solutions to the inequality considered as well as we suggest the Ritz type numerical approximations. The theoretical results obtained are next applied to some problems inspired by models from contact mechanics.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140900872","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 entropy solutions to a degenerate parabolic–parabolic chemotaxis system for flux-limited dispersal","authors":"Anna Zhigun","doi":"10.1016/j.nonrwa.2024.104132","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104132","url":null,"abstract":"<div><p>Existence of global finite-time bounded entropy solutions to a parabolic–parabolic system proposed in Bellomo et al. (2010) is established in bounded domains under no-flux boundary conditions for nonnegative bounded initial data. This modification of the classical Keller–Segel model features degenerate diffusion and chemotaxis that are both subject to flux-saturation. The approach is based on Schauder’s fixed point theorem and calculus of functions of bounded variation.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140843459","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":"On the number of limit cycles in piecewise planar quadratic differential systems","authors":"Francisco Braun ,&nbsp;Leonardo Pereira Costa da Cruz ,&nbsp;Joan Torregrosa","doi":"10.1016/j.nonrwa.2024.104124","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104124","url":null,"abstract":"<div><p>We consider piecewise quadratic perturbations of centers of piecewise quadratic systems in two zones determined by a straight line through the origin. By means of expansions of the displacement map, we are able to find isolated zeros of it, without dealing with the unsurprising difficult integrals inherent in the usual averaging approach. We apply this technique to non-smooth perturbations of the four families of isochronous centers of the Loud family, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, as well as to non-smooth perturbations of non-smooth centers given by putting different <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>’s in each zone. To show the coverage of our approach, we apply its first order, which is equivalent to averaging theory of the first order, in perturbations of the already mentioned centers considering all the straight lines through the origin. Then we apply the second order of our approach to perturbations of the above centers for a specific oblique straight line. Here in order to argue we introduce certain blow-ups in the perturbative parameters. As a consequence of our study, we obtain examples of piecewise quadratic systems with at least 12 limit cycles. By analyzing two previous works of the literature claiming much more limit cycles we found some mistakes in the calculations. Therefore, the best lower bound for the number of limit cycles of a piecewise quadratic system is up to now the 12 limit cycles found in the present paper.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140824129","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":"Optimal decay estimate and asymptotic profile for solutions to the generalized Zakharov–Kuznetsov–Burgers equation in 2D","authors":"Ikki Fukuda ,&nbsp;Hiroyuki Hirayama","doi":"10.1016/j.nonrwa.2024.104130","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104130","url":null,"abstract":"<div><p>We consider the Cauchy problem for the generalized Zakharov–Kuznetsov–Burgers equation in 2D. This is one of the nonlinear dispersive–dissipative equations, which has a spatial anisotropic dissipative term <span><math><mrow><mo>−</mo><mi>μ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub></mrow></math></span>. In this paper, we prove that the solution to this problem decays at the rate of <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></math></span> in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-sense, provided that the initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span> satisfies <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and some appropriate regularity assumptions. Moreover, we investigate the more detailed large time behavior and obtain a lower bound of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm of the solution. As a result, we prove that the given decay rate <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></math></span> of the solution to be optimal. Furthermore, combining the techniques used for the parabolic equations and for the Schr<span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>̈</mo></mrow></mover></math></span>dinger equation, we derive the explicit asymptotic profile for the solution.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825738","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":"Spatio-temporal patterns and global bifurcation of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses","authors":"Demou Luo ,&nbsp;Qiru Wang","doi":"10.1016/j.nonrwa.2024.104133","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104133","url":null,"abstract":"<div><p>The aim of this article is investigating the spatio-temporal patterns of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses. First, by utilizing user-friendly version of Crandall–Rabinowitz bifurcation theory as an analytical method, the spatio-temporal patterns of positive steady state are obtained. Then, by regarding the cross-diffusion coefficient <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> as a bifurcation parameter, we will derive a bifurcation theorem for the corresponding nonlinear cross-diffusion model. Moreover, by applying spectrum theory, perturbation of simple eigenvalues and linearized stability, it is discovered that the bifurcation solutions possess local stability near the bifurcating point in proper conditions. These theoretical results mean that the cross-diffusion mechanism can create a coexistence environment for the preys and predator under some circumstances. Finally, a numerical example is proposed to verify our results.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825739","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 role of manipulative trophically transmitted parasites in the stability of a predator–prey community","authors":"Jean-Christophe Poggiale ,&nbsp;Rafael Bravo de la Parra ,&nbsp;Ezio Venturino","doi":"10.1016/j.nonrwa.2024.104123","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104123","url":null,"abstract":"<div><p>In this paper, we are interested in the effect of a trophically transmitted parasite on the structure and dynamics of a resident predator–prey community. The parasite, apart from increasing the mortality rates of its hosts, can also change their physiology or their behaviour, which is known as trait-mediated indirect interaction. We assume that parasite transmission, which entails rapid physiological or behavioural change, is a fast process with respect to the community dynamics, including prey and predator growths and predation. This existence of different time scales allows us to provide analytical results to understand some conditions under which the parasite change the dynamics of the predator–prey community. Thus, we are able to find conditions under which indirect trait-mediated interactions induced by the parasite lead to a coexistence between predators and prey that would not occur in its absence. We also provide conditions, evolutionary deleterious, that ensure the extinction of a predator–prey community that would be viable without parasite intervention. Finally, we show situations in which the action of the parasite destabilizes the predator–prey system without eliminating it, producing oscillations, the mechanism of which is analysed.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824000634/pdfft?md5=c007706a979b3aa387e052c31cc79141&pid=1-s2.0-S1468121824000634-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140816717","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}