This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows up.
{"title":"High multiplicity and global structure of coexistence states in a predator-prey model with saturation","authors":"Kousuke Kuto , Julián López-Gómez , Eduardo Muñoz-Hernández","doi":"10.1016/j.jde.2026.114116","DOIUrl":"10.1016/j.jde.2026.114116","url":null,"abstract":"<div><div>This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows up.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114116"},"PeriodicalIF":2.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001827","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}
Pub Date : 2026-01-20DOI: 10.1016/j.jde.2026.114129
Lassi Paunonen , David Seifert
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and suitable conditions on the non-linearity. We illustrate the strength of our abstract results by applying them to a one-dimensional wave equation with weak non-linear damping and to an Euler–Bernoulli beam with a tip mass subject to non-linear damping.
{"title":"Polynomial stability of non-linearly damped contraction semigroups","authors":"Lassi Paunonen , David Seifert","doi":"10.1016/j.jde.2026.114129","DOIUrl":"10.1016/j.jde.2026.114129","url":null,"abstract":"<div><div>We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and suitable conditions on the non-linearity. We illustrate the strength of our abstract results by applying them to a one-dimensional wave equation with weak non-linear damping and to an Euler–Bernoulli beam with a tip mass subject to non-linear damping.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114129"},"PeriodicalIF":2.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034392","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}
Pub Date : 2026-01-20DOI: 10.1016/j.jde.2026.114124
Lucio Galeati , James-Michael Leahy , Torstein Nilssen
Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-posedness and existence of a flow for RDEs with Osgood drifts, as well as well-posedness of weak -valued solutions to linear rough continuity and transport equations on under DiPerna–Lions regularity conditions; a combination of the two then yields flow representation formulas for linear RPDEs. We apply these results to obtain existence, uniqueness and continuous dependence for -valued solutions to a general class of nonlinear continuity equations. In particular, our framework covers the 2D Euler equations in vorticity form with rough transport noise, providing a rough analogue of Yudovich's theorem. As a consequence, we construct an associated continuous random dynamical system, when the driving noise is a fractional Brownian motion with Hurst parameter . We further prove weak existence of solutions for initial vorticities in , for any .
{"title":"On the well-posedness of (nonlinear) rough continuity equations","authors":"Lucio Galeati , James-Michael Leahy , Torstein Nilssen","doi":"10.1016/j.jde.2026.114124","DOIUrl":"10.1016/j.jde.2026.114124","url":null,"abstract":"<div><div>Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-posedness and existence of a flow for RDEs with Osgood drifts, as well as well-posedness of weak <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-valued solutions to linear rough continuity and transport equations on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> under DiPerna–Lions regularity conditions; a combination of the two then yields flow representation formulas for linear RPDEs. We apply these results to obtain existence, uniqueness and continuous dependence for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-valued solutions to a general class of nonlinear continuity equations. In particular, our framework covers the 2D Euler equations in vorticity form with rough transport noise, providing a rough analogue of Yudovich's theorem. As a consequence, we construct an associated continuous random dynamical system, when the driving noise is a fractional Brownian motion with Hurst parameter <span><math><mi>H</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We further prove weak existence of solutions for initial vorticities in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>, for any <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114124"},"PeriodicalIF":2.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001826","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}
Pub Date : 2026-01-19DOI: 10.1016/j.jde.2026.114125
Song Jiang , Chunhui Zhou
We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flows between two moving parallel walls. Under the assumption , we prove that for any plane supersonic shear flow , there exist smooth solutions near to steady compressible Navier-Stokes equations in a 2-dimension domain . Moreover, based on the uniform-in-ε estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations.
{"title":"Structure stability of steady supersonic shear flow with inflow boundary conditions","authors":"Song Jiang , Chunhui Zhou","doi":"10.1016/j.jde.2026.114125","DOIUrl":"10.1016/j.jde.2026.114125","url":null,"abstract":"<div><div>We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flows between two moving parallel walls. Under the assumption <span><math><mn>0</mn><mo><</mo><mi>L</mi><mo>≪</mo><mn>1</mn></math></span>, we prove that for any plane supersonic shear flow <span><math><msup><mrow><mi>U</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>=</mo><mo>(</mo><mi>μ</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>,</mo><mn>0</mn><mo>)</mo></math></span>, there exist smooth solutions near <span><math><msup><mrow><mi>U</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> to steady compressible Navier-Stokes equations in a 2-dimension domain <span><math><mi>Ω</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>L</mi><mo>)</mo><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>. Moreover, based on the uniform-in-<em>ε</em> estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"458 ","pages":"Article 114125"},"PeriodicalIF":2.3,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023157","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}
Pub Date : 2026-01-19DOI: 10.1016/j.jde.2026.114105
Mohameden Ahmedou , Mohamed Ben Ayed , Khalil El Mehdi
Given a smooth positive function K on the standard sphere , we use Morse theoretical methods and counting index formulae to prove that, under generic conditions on the function K, there are arbitrarily many metrics g conformally equivalent to and whose scalar curvature is given by the function K provided that the function is sufficiently close to the scalar curvature of . Our approach leverages a comprehensive characterization of blowing-up solutions of a subcritical approximation, along with various Morse relations involving their indices. Notably, this multiplicity result is achieved without relying on any symmetry or periodicity assumptions about the function K.
{"title":"On the Nirenberg problem on spheres: Arbitrarily many solutions in a perturbative setting","authors":"Mohameden Ahmedou , Mohamed Ben Ayed , Khalil El Mehdi","doi":"10.1016/j.jde.2026.114105","DOIUrl":"10.1016/j.jde.2026.114105","url":null,"abstract":"<div><div>Given a smooth positive function <em>K</em> on the standard sphere <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>, we use Morse theoretical methods and counting index formulae to prove that, under generic conditions on the function <em>K</em>, there are arbitrarily many metrics <em>g</em> conformally equivalent to <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and whose scalar curvature is given by the function <em>K</em> provided that the function is sufficiently close to the scalar curvature of <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Our approach leverages a comprehensive characterization of blowing-up solutions of a subcritical approximation, along with various Morse relations involving their indices. Notably, this multiplicity result is achieved without relying on any symmetry or periodicity assumptions about the function <em>K</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114105"},"PeriodicalIF":2.3,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036009","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}
Pub Date : 2026-01-16DOI: 10.1016/j.jde.2026.114114
Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang
This paper is concerned with the inverse source problems for the acoustic wave equation in the full space , where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the -norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.
{"title":"Increasing stability for inverse acoustic source problems in the time domain","authors":"Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang","doi":"10.1016/j.jde.2026.114114","DOIUrl":"10.1016/j.jde.2026.114114","url":null,"abstract":"<div><div>This paper is concerned with the inverse source problems for the acoustic wave equation in the full space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114114"},"PeriodicalIF":2.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980596","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}
Pub Date : 2026-01-16DOI: 10.1016/j.jde.2026.114115
Hilário Alencar , G. Pacelli Bessa , Gregório Silva Neto
In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the -mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the -mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the -mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.
{"title":"Half-space theorems for translating solitons of the r-mean curvature flow","authors":"Hilário Alencar , G. Pacelli Bessa , Gregório Silva Neto","doi":"10.1016/j.jde.2026.114115","DOIUrl":"10.1016/j.jde.2026.114115","url":null,"abstract":"<div><div>In this paper, we establish nonexistence results for complete translating solitons of the <em>r</em>-mean curvature flow under suitable growth conditions on the <span><math><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the <span><math><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the <span><math><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114115"},"PeriodicalIF":2.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977987","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}
Pub Date : 2026-01-16DOI: 10.1016/j.jde.2026.114103
Tomás Caraballo , Alexandre N. Carvalho , Arthur C. Cunha , Heraclio López-Lázaro
In this paper, we introduce the concept of uniformly differentiable evolution processes for dynamical systems on families of time-dependent phase spaces. This framework is motivated by two main aspects: it provides an appropriate framework for studying the dynamics of solutions to non-cylindrical PDE problems, and it naturally extends the theory of uniformly differentiable evolution processes on fixed phase spaces. We establish sufficient conditions on the differential of the evolution process, decomposed as the sum of a contraction and an operator with compactness properties, ensuring that the associated pullback attractors have finite fractal dimension. Our approach is inspired by the smoothing property, Mañé's method, and techniques for controlling backward bounded trajectories. As an application, we analyze non-cylindrical problems with different geometries, studying the dynamics of solutions for the one-dimensional semilinear heat equation and for the two-dimensional Navier-Stokes equations.
{"title":"Smoothing property assumptions for uniformly differential processes acting on time-dependent normed spaces","authors":"Tomás Caraballo , Alexandre N. Carvalho , Arthur C. Cunha , Heraclio López-Lázaro","doi":"10.1016/j.jde.2026.114103","DOIUrl":"10.1016/j.jde.2026.114103","url":null,"abstract":"<div><div>In this paper, we introduce the concept of uniformly differentiable evolution processes for dynamical systems on families of time-dependent phase spaces. This framework is motivated by two main aspects: it provides an appropriate framework for studying the dynamics of solutions to non-cylindrical PDE problems, and it naturally extends the theory of uniformly differentiable evolution processes on fixed phase spaces. We establish sufficient conditions on the differential of the evolution process, decomposed as the sum of a contraction and an operator with compactness properties, ensuring that the associated pullback attractors have finite fractal dimension. Our approach is inspired by the smoothing property, Mañé's method, and techniques for controlling backward bounded trajectories. As an application, we analyze non-cylindrical problems with different geometries, studying the dynamics of solutions for the one-dimensional semilinear heat equation and for the two-dimensional Navier-Stokes equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114103"},"PeriodicalIF":2.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977970","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}
Pub Date : 2026-01-16DOI: 10.1016/j.jde.2026.114111
Fucai Li , Houzhi Tang , Shuxing Zhang
The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction named Cattaneo's law was proposed, which leads to the finite speed of heat propagation. A natural question is whether the large-time behavior of the heat flux for compressible flow would be different for these two laws. In this paper, we aim to address this question by studying the global well-posedness and the optimal time-decay rates of classical solutions to the compressible Navier-Stokes system with Cattaneo's law. By designing a new method, we obtain the optimal time-decay rates for the highest order derivatives of the heat flux, which cannot be derived for the system with Fourier's law by Matsumura and Nishida (1979) [25]. In this sense, our results first reveal the essential differences between the two laws.
{"title":"Global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction","authors":"Fucai Li , Houzhi Tang , Shuxing Zhang","doi":"10.1016/j.jde.2026.114111","DOIUrl":"10.1016/j.jde.2026.114111","url":null,"abstract":"<div><div>The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction named Cattaneo's law was proposed, which leads to the finite speed of heat propagation. A natural question is whether the large-time behavior of the heat flux for compressible flow would be different for these two laws. In this paper, we aim to address this question by studying the global well-posedness and the optimal time-decay rates of classical solutions to the compressible Navier-Stokes system with Cattaneo's law. By designing a new method, we obtain the optimal time-decay rates for the highest order derivatives of the heat flux, which cannot be derived for the system with Fourier's law by Matsumura and Nishida (1979) <span><span>[25]</span></span>. In this sense, our results first reveal the essential differences between the two laws.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114111"},"PeriodicalIF":2.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977986","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}
Pub Date : 2026-01-16DOI: 10.1016/j.jde.2026.114107
Wanxiao Xu , Hongying Shu , Lin Wang , Xiang-Sheng Wang , Jianshe Yu
Incorporating spatial diffusion and digestion delay into an intraguild predation (IGP) model, this work demonstrates rich spatiotemporal dynamics governing biological invasions. We derive criteria for the successful invasion of the intraguild predator and identify a critical diffusion threshold that eliminates spatially heterogeneous steady states. The digestion delay induces stability switches, resulting in a finite number of stability intervals, and causing abrupt shifts in coexistence patterns as the delay crosses critical thresholds. Through steady state bifurcation analysis, we rigorously establish the emergence of spatially heterogeneous coexistence states. We further derive Turing instability conditions for Hopf-bifurcating periodic solutions in a general three-dimensional delayed diffusive system. Our results reveal multiple coexistence mechanisms, including homogeneous steady states, periodic oscillations, and complex spatiotemporal patterns, highlighting the intricate interplay between time delay and spatial heterogeneity in biological invasions.
{"title":"Complex spatiotemporal dynamics in a diffusive intraguild predation model with digestion delay","authors":"Wanxiao Xu , Hongying Shu , Lin Wang , Xiang-Sheng Wang , Jianshe Yu","doi":"10.1016/j.jde.2026.114107","DOIUrl":"10.1016/j.jde.2026.114107","url":null,"abstract":"<div><div>Incorporating spatial diffusion and digestion delay into an intraguild predation (IGP) model, this work demonstrates rich spatiotemporal dynamics governing biological invasions. We derive criteria for the successful invasion of the intraguild predator and identify a critical diffusion threshold that eliminates spatially heterogeneous steady states. The digestion delay induces stability switches, resulting in a finite number of stability intervals, and causing abrupt shifts in coexistence patterns as the delay crosses critical thresholds. Through steady state bifurcation analysis, we rigorously establish the emergence of spatially heterogeneous coexistence states. We further derive Turing instability conditions for Hopf-bifurcating periodic solutions in a general three-dimensional delayed diffusive system. Our results reveal multiple coexistence mechanisms, including homogeneous steady states, periodic oscillations, and complex spatiotemporal patterns, highlighting the intricate interplay between time delay and spatial heterogeneity in biological invasions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114107"},"PeriodicalIF":2.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980541","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}
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