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Well-posedness of Keller-Segel systems on compact metric graphs.
IF 1.1 3区 数学
Journal of Evolution Equations Pub Date : 2025-01-01 Epub Date: 2024-12-15 DOI: 10.1007/s00028-024-01033-x
Hewan Shemtaga, Wenxian Shen, Selim Sukhtaiev
{"title":"Well-posedness of Keller-Segel systems on compact metric graphs.","authors":"Hewan Shemtaga, Wenxian Shen, Selim Sukhtaiev","doi":"10.1007/s00028-024-01033-x","DOIUrl":"https://doi.org/10.1007/s00028-024-01033-x","url":null,"abstract":"<p><p>Chemotaxis phenomena govern the directed movement of microorganisms in response to chemical stimuli. In this paper, we investigate two Keller-Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks. The distinction between two systems is driven by the rate of diffusion of the chemo-attractant. The intermediate rate of diffusion is modeled by a coupled pair of parabolic equations, while the rapid rate is described by a parabolic equation coupled with an elliptic one. Assuming the polynomial rate of growth of the chemotaxis sensitivity coefficient, we prove local well-posedness of both systems on compact metric graphs, and, in particular, prove existence of unique classical solutions. This is achieved by constructing sufficiently regular mild solutions via analytic semigroup methods and combinatorial description of the heat kernel on metric graphs. The regularity of mild solutions is shown by applying abstract semigroup results to semi-linear parabolic equations on compact graphs. In addition, for logistic-type Keller-Segel systems we prove global well-posedness and, in some special cases, global uniform boundedness of solutions.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 1","pages":"7"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646970/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142848398","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}
引用次数: 0
A higher-order quadratic NLS equation on the half-line.
IF 1.1 3区 数学
Journal of Evolution Equations Pub Date : 2025-01-01 Epub Date: 2024-12-15 DOI: 10.1007/s00028-024-01034-w
A Alexandrou Himonas, Fangchi Yan
{"title":"A higher-order quadratic NLS equation on the half-line.","authors":"A Alexandrou Himonas, Fangchi Yan","doi":"10.1007/s00028-024-01034-w","DOIUrl":"https://doi.org/10.1007/s00028-024-01034-w","url":null,"abstract":"<p><p>The well-posedness of the initial-boundary value problem for higher-order quadratic nonlinear Schrödinger equations on the half-line is studied by utilizing the Fokas solution formula for the corresponding linear problem. Using this formula, linear estimates are derived in Bourgain spaces for initial data in spatial Sobolev spaces on the half-line and boundary data in temporal Sobolev spaces suggested by the time regularity of the linear initial value problem. Then, the needed bilinear estimates are derived and used for showing that the iteration map defined via the Fokas solution formula is a contraction in appropriate solution spaces. Finally, well-posedness is established for optimal Sobolev exponents in a way analogous to the case of the initial value problem on the whole line with solutions in classical Bourgain spaces.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 1","pages":"8"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646971/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142848397","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}
引用次数: 0
Log-Sobolev inequalities and hypercontractivity for Ornstein – Uhlenbeck evolution operators in infinite dimension 奥恩斯坦-乌伦贝克演化算子在无限维的对数-索博列夫不等式和超收缩性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-13 DOI: 10.1007/s00028-024-01005-1
Davide A. Bignamini, Paolo De Fazio
{"title":"Log-Sobolev inequalities and hypercontractivity for Ornstein – Uhlenbeck evolution operators in infinite dimension","authors":"Davide A. Bignamini, Paolo De Fazio","doi":"10.1007/s00028-024-01005-1","DOIUrl":"https://doi.org/10.1007/s00028-024-01005-1","url":null,"abstract":"<p>In an infinite-dimensional separable Hilbert space <i>X</i>, we study the realizations of Ornstein–Uhlenbeck evolution operators <span>(P_{s,t})</span> in the spaces <span>(L^p(X,gamma _t))</span>, <span>({gamma _t}_{tin mathbb {R}})</span> being a suitable evolution system of measures for <span>(P_{s,t})</span>. We prove hypercontractivity results, relying on suitable Log-Sobolev estimates. Among the examples, we consider the transition evolution operator associated with a non-autonomous stochastic parabolic PDE.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"213 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250120","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}
引用次数: 0
Some qualitative analysis for a parabolic equation with critical exponential nonlinearity 具有临界指数非线性的抛物方程的一些定性分析
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-12 DOI: 10.1007/s00028-024-01008-y
Qiang Lin, Binlin Zhang
{"title":"Some qualitative analysis for a parabolic equation with critical exponential nonlinearity","authors":"Qiang Lin, Binlin Zhang","doi":"10.1007/s00028-024-01008-y","DOIUrl":"https://doi.org/10.1007/s00028-024-01008-y","url":null,"abstract":"<p>In this paper, we show a blowup criterion of solution for a parabolic equation with critical exponential source and arbitrary positive initial energy, which generalizes the blowup conclusions in reference (Ishiwata et al. in J Evol Equ 21:1677–1716, 2021) for subcritical and critical initial energy cases that depend on the depth of the potential well. Additionally, the continuous dependence of the local solution on the initial data is proved in detail.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"5 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186935","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}
引用次数: 0
Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity 活塞在粘性随密度变化的流体中运动的数学分析
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-07 DOI: 10.1007/s00028-024-01006-0
Vaibhav Kumar Jena, Debayan Maity, Abu Sufian
{"title":"Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity","authors":"Vaibhav Kumar Jena, Debayan Maity, Abu Sufian","doi":"10.1007/s00028-024-01006-0","DOIUrl":"https://doi.org/10.1007/s00028-024-01006-0","url":null,"abstract":"<p>We study a free boundary value problem modelling the motion of a piston in a viscous compressible fluid. The fluid is modelled by 1D compressible Navier–Stokes equations with possibly degenerate viscosity coefficient, and the motion of the piston is described by Newton’s second law. We show that the initial boundary value problem has a unique global in time solution, and we also determine the large time behaviour of the system. Finally, we show how our methodology may be adapted to the motion of several pistons.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"46 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186949","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}
引用次数: 0
Asymptotically almost periodic solutions for some partial differential inclusions in $$alpha $$ -norm $$alpha $$ -norm中某些偏微分夹杂的近似近周期解
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-07 DOI: 10.1007/s00028-024-01007-z
Mohamed Alia, Jaouad El Matloub, Khalil Ezzinbi
{"title":"Asymptotically almost periodic solutions for some partial differential inclusions in $$alpha $$ -norm","authors":"Mohamed Alia, Jaouad El Matloub, Khalil Ezzinbi","doi":"10.1007/s00028-024-01007-z","DOIUrl":"https://doi.org/10.1007/s00028-024-01007-z","url":null,"abstract":"<p>In this paper, we focus on investigating the existence of mild solutions and asymptotically almost periodic mild solutions for a class of partial differential inclusions. These inclusions involve a forcing multivalued function that relies on implicit spatial derivatives of the state variable. We introduce a novel approach to simplify the complexities associated with singularities when taking the <span>(alpha )</span>-norm.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186936","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}
引用次数: 0
Periodic motions of species competition flows and inertial manifolds around them with nonautonomous diffusion 非自主扩散的物种竞争流及其周围惯性流形的周期运动
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-02 DOI: 10.1007/s00028-024-00997-0
Thi Ngoc Ha Vu, Thieu Huy Nguyen
{"title":"Periodic motions of species competition flows and inertial manifolds around them with nonautonomous diffusion","authors":"Thi Ngoc Ha Vu, Thieu Huy Nguyen","doi":"10.1007/s00028-024-00997-0","DOIUrl":"https://doi.org/10.1007/s00028-024-00997-0","url":null,"abstract":"<p>Motivated by the competition model of two species with nonautonomous diffusion, we consider fully nonautonomous parabolic evolution equation of the form <span>(frac{textrm{d}u}{textrm{d}t} + A(t)u(t) = f(t,u)+g(t))</span> in which the time-dependent family of linear partial differential operator <i>A</i>(<i>t</i>), the nonlinear term <i>f</i>(<i>t</i>, <i>u</i>), and the external force <i>g</i> is 1-periodic with respect to <i>t</i>. We prove the existence and uniqueness of a periodic solution of the above equation and study the inertial manifold for the solutions nearby that solution. We prove the existence of such an inertial manifold in the cases that the family of linear partial differential operators <span>((A(t))_{tin mathbb {R}})</span> generates an evolution family <span>((U(t,s))_{tge s})</span> satisfying certain dichotomy estimates, and the nonlinear term <i>f</i>(<i>t</i>, <i>x</i>) satisfies the <span>(varphi )</span>-Lipschitz condition, i.e., <span>(left| f(t,x_1)-f(t,x_2)right| leqslant varphi (t)left| A(t)^{theta } (x_1-x_2)right| )</span> where <span>(varphi (cdot ))</span> belongs to some admissible function space on the whole line. Then, we apply our abstract results to the above-mentioned competition model of two species with nonautonomous diffusion.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"2022 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186951","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}
引用次数: 0
Fine large-time asymptotics for the axisymmetric Navier–Stokes equations 轴对称纳维-斯托克斯方程的精细大时间渐近线
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-27 DOI: 10.1007/s00028-024-01001-5
Christian Seis, Dominik Winkler
{"title":"Fine large-time asymptotics for the axisymmetric Navier–Stokes equations","authors":"Christian Seis, Dominik Winkler","doi":"10.1007/s00028-024-01001-5","DOIUrl":"https://doi.org/10.1007/s00028-024-01001-5","url":null,"abstract":"<p>We examine the large-time behavior of axisymmetric solutions without swirl of the Navier–Stokes equation in <span>({mathbb {R}}^3)</span>. We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in the simplicity of the applied techniques: Our approach is completely based on standard <span>(L^2)</span>-based entropy methods.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"5 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186952","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}
引用次数: 0
Another remark on the global regularity issue of the Hall-magnetohydrodynamics system 关于霍尔磁流体动力学系统全局正则性问题的另一个评论
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-24 DOI: 10.1007/s00028-024-01000-6
Mohammad Mahabubur Rahman, Kazuo Yamazaki
{"title":"Another remark on the global regularity issue of the Hall-magnetohydrodynamics system","authors":"Mohammad Mahabubur Rahman, Kazuo Yamazaki","doi":"10.1007/s00028-024-01000-6","DOIUrl":"https://doi.org/10.1007/s00028-024-01000-6","url":null,"abstract":"<p>We discover new cancellations upon <span>(H^{2}(mathbb {R}^{n}))</span>-estimate of the Hall term, <span>(n in {2,3})</span>. Consequently, first, we derive a regularity criterion for the 3-dimensional Hall-magnetohydrodynamics system in terms of horizontal components of velocity and magnetic fields. Second, we are able to prove the global regularity of the <span>(2frac{1}{2})</span>-dimensional electron magnetohydrodynamics system with magnetic diffusion <span>((-Delta )^{frac{3}{2}} (b_{1}, b_{2}, 0) + (-Delta )^{alpha } (0, 0, b_{3}))</span> for <span>(alpha &gt; frac{1}{2})</span> despite the fact that <span>((-Delta )^{frac{3}{2}})</span> is the critical diffusive strength. Lastly, we extend this result to the <span>(2frac{1}{2})</span>-dimensional Hall-magnetohydrodynamics system with <span>(-Delta u)</span> replaced by <span>((-Delta )^{alpha } (u_{1}, u_{2}, 0) -Delta (0, 0, u_{3}))</span> for <span>(alpha &gt; frac{1}{2})</span>. The sum of the derivatives in diffusion that our result requires is <span>(11+ epsilon )</span> for any <span>(epsilon &gt; 0)</span>, while the sum for the classical <span>(2frac{1}{2})</span>-dimensional Hall-magnetohydrodynamics system is 12 considering <span>(-Delta u)</span> and <span>(-Delta b)</span>, of which its global regularity issue remains an outstanding open problem.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186953","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}
引用次数: 0
Global strong solutions with large oscillations to the 3D full compressible Navier–Stokes equations without heat conductivity 无热传导的三维全可压缩纳维-斯托克斯方程具有大振荡的全局强解
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-24 DOI: 10.1007/s00028-024-01002-4
Haibo Yu
{"title":"Global strong solutions with large oscillations to the 3D full compressible Navier–Stokes equations without heat conductivity","authors":"Haibo Yu","doi":"10.1007/s00028-024-01002-4","DOIUrl":"https://doi.org/10.1007/s00028-024-01002-4","url":null,"abstract":"<p>We are concerned with the Cauchy problem to the three-dimensional full compressible Navier–Stokes equations with zero heat conductivity. Under the condition that the initial energy is small enough, global existence of strong solutions is established. Especially, the initial density is allowed to have large oscillations. The key to estimate the pointwise lower and upper bounds of the density lies in the handling of the energy conservation equation and the boundedness of the <span>(L^r)</span>–norm of the gradient of the pressure.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"46 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186954","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}
引用次数: 0
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