Journal of Differential Equations最新文献

{"title":"On a scaled abstract linking theorem with an application to the Schrödinger–Poisson–Slater equation","authors":"Kanishka Perera ,&nbsp;Kaye Silva","doi":"10.1016/j.jde.2025.113824","DOIUrl":"10.1016/j.jde.2025.113824","url":null,"abstract":"<div><div>We prove an abstract linking theorem that can be used to show existence of solutions to various types of variational elliptic equations, including Schrödinger–Poisson–Slater type equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113824"},"PeriodicalIF":2.3,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145236433","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}

{"title":"Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary","authors":"Yingzhi Du ,&nbsp;Tao Luo ,&nbsp;Xin Xu","doi":"10.1016/j.jde.2025.113801","DOIUrl":"10.1016/j.jde.2025.113801","url":null,"abstract":"<div><div>This paper investigates the uniform regularity of solutions to the compressible magnetohydrodynamics (MHD) system in the half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> in small Alfvén and Mach Numbers. The study focuses on the case where the magnetic field is tangential to the physical boundary, satisfying the perfect conducting boundary condition, while the velocity field adheres to a Navier-slip boundary condition. Under the condition that bounds the normal derivatives of the velocity and magnetic field uniformly in <em>ϵ</em> (the small Alfvén and Mach Numbers), we establish uniform estimates for the solutions in high-order conormal Sobolev norms. The results distinguish the previous works primarily addressing cases where the magnetic field is transversal to the boundary.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113801"},"PeriodicalIF":2.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223406","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}

{"title":"Singular limit and convergence rate via projection method in a model for plant-growth dynamics with autotoxicity","authors":"Jeff Morgan ,&nbsp;Cinzia Soresina ,&nbsp;Bao Quoc Tang ,&nbsp;Bao-Ngoc Tran","doi":"10.1016/j.jde.2025.113797","DOIUrl":"10.1016/j.jde.2025.113797","url":null,"abstract":"<div><div>We investigate a fast-reaction-diffusion system modeling the autotoxicity effect on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The model was proposed in [Giannino-Iuorio-Soresina, 2025] to account for stable stationary spatial patterns considering only biomass and toxicity, and its fast-reaction (cross-diffusion) limit was formally derived and numerically investigated. In this paper, the cross-diffusion limiting system is rigorously obtained as the fast-reaction limit of the reaction–diffusion system with fast-reaction terms by performing a bootstrap argument involving energies. Then, a thorough well-posedness analysis of the cross-diffusion system is presented, including an essential bound, uniqueness, stability, and regularity of weak solutions. This analysis, in turn, becomes crucial to establish the convergence rate for the fast-reaction limit, thanks to the key idea of using an inverse Neumann Laplacian operator. Finally, a numerical experiment illustrates the analytical findings on the convergence rate.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113797"},"PeriodicalIF":2.3,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222698","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}

{"title":"Existence and approximation of measure attractors and invariant measures for McKean-Vlasov stochastic lattice system with Lévy noise","authors":"Fan Bai,&nbsp;Zhang Chen,&nbsp;Xiaoxiao Sun","doi":"10.1016/j.jde.2025.113784","DOIUrl":"10.1016/j.jde.2025.113784","url":null,"abstract":"<div><div>This paper is devoted to the existence and approximation of measure attractors and invariant measures for superlinear McKean-Vlasov stochastic reaction-diffusion lattice system driven by Lévy noise. We firstly prove the well-posedness of solutions by the fixed point arguments. Then by the uniform pullback estimates and tail-ends estimates of solutions, we establish the pullback asymptotic compactness of non-autonomous dynamical systems generated by the solution operators in a space of probability measures, and further obtain the existence and upper semicontinuity of measure attractors. Moreover, we yield the existence and uniqueness of invariant measures as well as ergodicity of the solutions under additional conditions. In addition, the convergence rate of invariant measures is provided when distribution dependent stochastic system converges to distribution independent one. Finally, the finite-dimensional approximations of measure attractors and invariant measures are investigated between such lattice system and its finite-dimensional truncated system, which are useful for studying numerical invariant measures.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113784"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222214","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}

{"title":"Existence and nonlinear stability of stationary solutions to the outflow problem of the one-dimensional full compressible Navier-Stokes-Allen-Cahn system","authors":"Zhengzheng Chen ,&nbsp;Dan Lei ,&nbsp;Haiyan Yin","doi":"10.1016/j.jde.2025.113803","DOIUrl":"10.1016/j.jde.2025.113803","url":null,"abstract":"<div><div>This paper is concerned with the large-time behavior of solutions toward a stationary solution for the outflow problem of the full compressible Navier-Stokes-Allen-Cahn system in the half-space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>. The model can be used to describe the motion of a mixture of two viscous compressible fluids. First, we give some sufficient conditions for the existence of stationary solution via the manifold theory and the center manifold theory. Second, by using the elementary <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-energy method, it is shown that the stationary solution is time-asymptotically stable provided that the initial perturbation and the strength of the stationary solution are sufficiently small. Finally, the convergence rates of solutions towards the stationary one are also established by employing a time and space weighted energy method. Our analysis is based on some new techniques which take into account the effect of the phase field variable.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113803"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222211","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}

{"title":"The reflection coefficient of a fractional reflector","authors":"Laurent Demanet ,&nbsp;Olivier Lafitte","doi":"10.1016/j.jde.2025.113788","DOIUrl":"10.1016/j.jde.2025.113788","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper considers the question of characterizing the behavior of waves reflected by a fractional singularity of the wave speed profile, i.e., of the form&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; not necessarily integer. We first focus on the case of one spatial dimension and a harmonic time dependence. We define the reflection coefficient &lt;em&gt;R&lt;/em&gt; from a limiting absorption principle. We provide an exact formula for &lt;em&gt;R&lt;/em&gt; in terms of the solution to a Volterra equation. We obtain the asymptotic limit of this coefficient in the large &lt;span&gt;&lt;math&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; regime as&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;Γ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mtext&gt;lower order terms.&lt;/mtext&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; The amplitude is proportional to &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, and the phase rotation behavior is obtained from the &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; factor. The proof method does not rely on representing the solution by special functions, since &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is general.&lt;/div&gt;&lt;div&gt;In the multi-dimensional layered case, we obtain a similar result where the nondimensional variable &lt;span&gt;&lt;math&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is modified to account for the angle of incidence. The asymptotic analysis now requires the waves to be non-glancing. The resulting reflection coefficient can now be interpreted as a Fourier multiplier of order −&lt;em&gt;α&lt;/em&gt;.&lt;/div&gt;&lt;div&gt;In practice, the knowledge of the dependency of both the amplitude and the phase of &lt;em&gt;R&lt;/em&gt; on &lt;em&gt;ω&lt;/em&gt; and &lt;em&gt;α&lt;/em&gt; might be able to infor","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113788"},"PeriodicalIF":2.3,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223408","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}

{"title":"Threshold dynamics for the 3d radial NLS with combined nonlinearity","authors":"Alex H. Ardila ,&nbsp;Jason Murphy ,&nbsp;Jiqiang Zheng","doi":"10.1016/j.jde.2025.113800","DOIUrl":"10.1016/j.jde.2025.113800","url":null,"abstract":"<div><div>We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions:<span><span><span><math><mo>(</mo><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>Δ</mi><mo>)</mo><mi>u</mi><mo>=</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>−</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mi>u</mi><mo>.</mo></math></span></span></span> In <span><span>[18]</span></span>, the authors classified the dynamics of solutions under the energy constraint <span><math><mi>E</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>&lt;</mo><msup><mrow><mi>E</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>(</mo><mi>W</mi><mo>)</mo></math></span>, where <em>W</em> is the quintic NLS ground state and <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> is the quintic NLS energy. In this work we classify the dynamics of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> solutions at the threshold <span><math><mi>E</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>E</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>(</mo><mi>W</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113800"},"PeriodicalIF":2.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223407","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}

{"title":"Traveling motility of actin lamellar fragments under spontaneous symmetry breaking","authors":"Claudia García ,&nbsp;Martina Magliocca ,&nbsp;Nicolas Meunier","doi":"10.1016/j.jde.2025.113787","DOIUrl":"10.1016/j.jde.2025.113787","url":null,"abstract":"<div><div>Cell motility is connected to the spontaneous symmetry breaking of a circular shape. In <span><span>[8]</span></span>, Blanch-Mercader and Casademunt performed a nonlinear analysis of the minimal model proposed by Callan and Jones <span><span>[11]</span></span> and numerically conjectured the existence of traveling solutions once that symmetry is broken. In this work, we prove analytically that conjecture by means of nonlinear bifurcation techniques.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113787"},"PeriodicalIF":2.3,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156706","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}

{"title":"Theoretical analysis of canard dynamics in a nonlinear neuron model with reset","authors":"Qixiang Xu ,&nbsp;Jieqiong Xu ,&nbsp;Junjien Wang ,&nbsp;Jimin Qiu","doi":"10.1016/j.jde.2025.113799","DOIUrl":"10.1016/j.jde.2025.113799","url":null,"abstract":"<div><div>We present a mathematics analysis showing that bursting oscillation and its complex transitions caused by reset-induced canard cycles are generated in a class of Izhikevich quadratic models. Using geometric singular perturbation theory and asymptotic expansion with boundary layer function, the expressions of the attracting and repelling parts of the slow manifold as well as the flow solution of the system are obtained, which is convenient to compute the time when the flow reaches the threshold line and the reset line. Based on the above results, it is proven that the system can support bursts of any period and canard cycles of any period as a function of model parameters, and the <em>N</em> - reset periodic cycles (for <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span>) are asymptotically stable through constructing the Poincaré map. Finally, we prove that there is no chaos in the transition between <em>N</em> - and <span><math><mo>(</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> - reset periodic cycles when <em>ε</em> is in a certain small scope but it organized by canard cycles.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113799"},"PeriodicalIF":2.3,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156934","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}

{"title":"Boundedness of weak solutions to degenerate Kolmogorov equations of hypoelliptic type in bounded domains","authors":"Mingyi Hou","doi":"10.1016/j.jde.2025.113794","DOIUrl":"10.1016/j.jde.2025.113794","url":null,"abstract":"<div><div>We establish the boundedness of weak subsolutions for a class of degenerate Kolmogorov equations of the hypoelliptic type, compatible with a homogeneous Lie group structure, within bounded product domains using the De Giorgi iteration. We employ the renormalization formula to handle boundary values and provide energy estimates. An <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>–<span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> type embedding estimate derived from the fundamental solution is utilized to incorporate lower-order divergence terms. This work naturally extends the boundedness theory for uniformly parabolic equations, with matching exponents for the coefficients.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113794"},"PeriodicalIF":2.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156707","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}