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Global boundedness of solutions to a class of partial differential equations with time delay
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113232
Xuanyu Liu , Junping Shi , Chuncheng Wang , Dejun Fan
{"title":"Global boundedness of solutions to a class of partial differential equations with time delay","authors":"Xuanyu Liu ,&nbsp;Junping Shi ,&nbsp;Chuncheng Wang ,&nbsp;Dejun Fan","doi":"10.1016/j.jde.2025.113232","DOIUrl":"10.1016/j.jde.2025.113232","url":null,"abstract":"<div><div>A class of diffusive partial differential equations with strongly coupled time delays and diffusion is considered. The global boundedness of weak solutions of the equation is proved by an entropy method that was initially proposed for studying the global boundedness of reaction-diffusion equations with cross-diffusion. The presence of the time delays in the equation prevents the entropy method to be directly applied, and here we extend the entropy method to this class of diffusive partial differential equations with time delays by proving some key entropy inequalities, which further allows us to obtain the estimates of gradient of the solutions. The results can be used to show the global boundedness of solutions of population models with memory effect, which were recently proposed for describing the movement of highly-developed animal species. In addition, we show that the results are also applicable for the classic partial functional differential equations, where the time delays only appear in the reaction terms.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113232"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A simple way to well-posedness in H1 of a delay differential equation from cell biology
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113241
Bernhard Aigner , Marcus Waurick
{"title":"A simple way to well-posedness in H1 of a delay differential equation from cell biology","authors":"Bernhard Aigner ,&nbsp;Marcus Waurick","doi":"10.1016/j.jde.2025.113241","DOIUrl":"10.1016/j.jde.2025.113241","url":null,"abstract":"<div><div>We present an application of recent well-posedness results in the theory of delay differential equations for ordinary differential equations <span><span>[10]</span></span> to a generalized population model for stem cell maturation. The weak approach using Sobolev-spaces we take allows for a larger class of initial prehistories and makes checking the requirements for well-posedness of such a model considerably easier compared to previous approaches. In fact the present approach is a possible means to guarantee that the solution manifold is not empty, which is a necessary requirement for a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-approach to work.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113241"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sub-exponential localization for a random tight-binding model with long-range hopping
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113239
Siqi Xu , Dongfeng Yan
{"title":"Sub-exponential localization for a random tight-binding model with long-range hopping","authors":"Siqi Xu ,&nbsp;Dongfeng Yan","doi":"10.1016/j.jde.2025.113239","DOIUrl":"10.1016/j.jde.2025.113239","url":null,"abstract":"<div><div>In this paper, we study the Anderson tight-binding model on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with the sub-exponential long-range hopping and log-Hölder continuously distributed potential. It is proved that, at high disorder this model has pure point spectrum with sub-exponentially decaying eigenfunctions. This gives a partial answer to a conjecture of Yeung-Oono [<em>Europhys. Lett.</em> 4(9), (1987): 1061-1065]. Our proof is based on multi-scale analysis type Green's function estimates.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113239"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatio-temporal dynamics for cooperative reaction-diffusion systems with asymptotic annihilation
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113234
Tian Hou , Yi Wang , Xiao-Qiang Zhao
{"title":"Spatio-temporal dynamics for cooperative reaction-diffusion systems with asymptotic annihilation","authors":"Tian Hou ,&nbsp;Yi Wang ,&nbsp;Xiao-Qiang Zhao","doi":"10.1016/j.jde.2025.113234","DOIUrl":"10.1016/j.jde.2025.113234","url":null,"abstract":"<div><div>In this paper, we investigate the spatio-temporal dynamics for cooperative random diffusion and nonlocal dispersal systems with time-periodic shifting environment. Under the assumption that the edge of our habitat is shifting and both two limiting systems exhibit asymptotic annihilation, we firstly prove the spreading extinction of solutions. Then we establish the threshold dynamics of time-periodic forced wave via the asymptotic spectral radius, which is well-defined and admits a lower bound determined by an associated Dirichlet boundary value problem. Our analysis is mainly based on the recent theory developed for monotone evolution systems with asymptotic translation invariance.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113234"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Li-Lin's open problem
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113244
Zhi-Yun Tang, Xianhua Tang
{"title":"On Li-Lin's open problem","authors":"Zhi-Yun Tang,&nbsp;Xianhua Tang","doi":"10.1016/j.jde.2025.113244","DOIUrl":"10.1016/j.jde.2025.113244","url":null,"abstract":"<div><div>In this paper, we give a first negative answer to a question proposed by Li and Lin (2012) <span><span>[5]</span></span>. Meanwhile, we also give a second positive answer to the Li-Lin's open problem. The first positive answer was given by G. Cerami, X. Zhong and W. Zou (2015) <span><span>[2]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113244"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-time-scale stochastic functional differential equations: Inclusion of infinite delay and coupled segment processes
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113238
Fuke Wu , George Yin
{"title":"Two-time-scale stochastic functional differential equations: Inclusion of infinite delay and coupled segment processes","authors":"Fuke Wu ,&nbsp;George Yin","doi":"10.1016/j.jde.2025.113238","DOIUrl":"10.1016/j.jde.2025.113238","url":null,"abstract":"<div><div>This paper focuses on two-time-scale stochastic functional differential equations (SFDEs). It features in inclusion of infinite delay and coupling of slow and fast components. The coupling is through the segment processes of the slow and fast processes. The main difficulties include infinite delay and the coupling of segment processes involving fast and slow motions. Concentrating on weak convergence, the tightness of the segment process is established on a space of continuous functions. In addition, the Hölder continuity and boundedness for the segment process of the slow component, uniform boundedness for the segment process of a fixed-<em>x</em> SFDE, exponential ergodicity, and continuous dependence on parameters are obtained to carry out the desired asymptotic analysis, and also as byproducts, which are interesting in their own right. Then using the martingale problem formulation, an average principle is established by a direct averaging, which involves detailed computations and subtle estimates. Finally, two classes of special SFDEs, stochastic integro-differential equations and stochastic delay differential equations with two-time scales are investigated.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113238"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact multiplicity, bifurcation curves, and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-19 DOI: 10.1016/j.jde.2025.113226
Rachidi B. Salako , Yixiang Wu , Shuwen Xue
{"title":"Exact multiplicity, bifurcation curves, and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model","authors":"Rachidi B. Salako ,&nbsp;Yixiang Wu ,&nbsp;Shuwen Xue","doi":"10.1016/j.jde.2025.113226","DOIUrl":"10.1016/j.jde.2025.113226","url":null,"abstract":"<div><div>This study examines the global structure of endemic equilibrium (EE) solutions of a cross-diffusive epidemic model which incorporates the repulsive movement of the susceptible population away from the infected population. We show that the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> alone cannot determine the existence of the EEs and the model may have multiple EEs when the repulsive movement rate <em>χ</em> is large. We prove that the set of EEs forms a simple and unbounded curve bifurcating from the curve of disease free equilibria at <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span> as <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> varies from zero to infinity, where the bifurcation curve can be forward or backward. We find conditions under which a forward bifurcation curve is of S-shaped and show that a large <em>χ</em> tends to induce backward bifurcation curves. Results on the asymptotic profiles of the EEs are obtained as the repulsive movement rate is large or the random movement rates are small. Finally, we perform numerical simulations to illustrate the results.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113226"},"PeriodicalIF":2.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shifts on trees versus classical shifts in chain recurrence
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-19 DOI: 10.1016/j.jde.2025.113230
Antoni López-Martínez , Dimitris Papathanasiou
{"title":"Shifts on trees versus classical shifts in chain recurrence","authors":"Antoni López-Martínez ,&nbsp;Dimitris Papathanasiou","doi":"10.1016/j.jde.2025.113230","DOIUrl":"10.1016/j.jde.2025.113230","url":null,"abstract":"<div><div>We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not chain recurrent operators. This construction completely solves in the negative a problem posed by Nilson C. Bernardes Jr. and Alfred Peris on chain recurrence in Linear Dynamics. In particular: we show that the non-invertible case can be directly solved via relatively simple weighted backward shifts acting on certain unrooted directed trees; then we modify the non-invertible counterexample to address the invertible case, but falling outside the class of weighted shift operators; and we finally show that this behaviour cannot be achieved via classical (unilateral neither bilateral) weighted backward sifts (acting on <span><math><mi>N</mi></math></span> and <span><math><mi>Z</mi></math></span> respectively) by noticing that a classical shift is a chain recurrent operator as soon as it admits a non-zero chain recurrent vector.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113230"},"PeriodicalIF":2.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global bifurcation results for a delay differential system representing a chemostat model
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-19 DOI: 10.1016/j.jde.2025.113222
Pablo Amster , Pierluigi Benevieri
{"title":"Global bifurcation results for a delay differential system representing a chemostat model","authors":"Pablo Amster ,&nbsp;Pierluigi Benevieri","doi":"10.1016/j.jde.2025.113222","DOIUrl":"10.1016/j.jde.2025.113222","url":null,"abstract":"<div><div>This paper studies a one-species chemostat model described by a system of differential delay equations, featuring a periodic input of a single nutrient with period <em>ω</em>. The delay represents the interval time between the consumption of the nutrient and its metabolization by the microbial species. We obtain global bifurcation results for the periodic solutions with period <em>ω</em>. Our proof is based on the application of the topological degree theory combined with a Whyburn-type Lemma.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113222"},"PeriodicalIF":2.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143641155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and regularity results for the penalized thin obstacle problem with variable coefficients
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-19 DOI: 10.1016/j.jde.2025.02.084
Donatella Danielli , Brian Krummel
{"title":"Existence and regularity results for the penalized thin obstacle problem with variable coefficients","authors":"Donatella Danielli ,&nbsp;Brian Krummel","doi":"10.1016/j.jde.2025.02.084","DOIUrl":"10.1016/j.jde.2025.02.084","url":null,"abstract":"<div><div>In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and optimal regularity of solutions, and establish structural properties of the free boundary. The proofs are based on tailor-made monotonicity formulas of Almgren, Weiss, and Monneau-type, combined with the classical theory of oblique derivative problems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113213"},"PeriodicalIF":2.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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