Journal of Evolution Equations最新文献

{"title":"Trace theory for parabolic boundary value problems with rough boundary conditions.","authors":"Robert Denk, Floris B Roodenburg","doi":"10.1007/s00028-026-01226-6","DOIUrl":"10.1007/s00028-026-01226-6","url":null,"abstract":"<p><p>We characterize the trace spaces arising from intersections of weighted, vector-valued Sobolev spaces, where the weights are powers of the distance to the boundary. These weighted function spaces are particularly suitable for treating boundary value problems where derivatives of the solution blow up at the boundary. As an application of our trace theory, we prove well-posedness for the heat equation with rough inhomogeneous boundary data in Sobolev spaces of higher regularity in domains of fixed regularity <math><msup><mi>C</mi> <mrow><mn>1</mn> <mo>,</mo> <mi>κ</mi></mrow> </msup> </math> , with <math><mrow><mi>κ</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></mrow> </math> .</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"26 3","pages":"80"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13236733/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148201125","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":"Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation.","authors":"Justin Forlano","doi":"10.1007/s00028-026-01237-3","DOIUrl":"10.1007/s00028-026-01237-3","url":null,"abstract":"<p><p>We extend recent results of Genovese-Luca-Tzvetkov (2022) regarding the quasi-invariance of Gaussian measures under the flow of the periodic Benjamin-Ono-BBM (BO-BBM) equation to the full range where BO-BBM is globally well-posed. The main difficulty is due to the critical nature of the dispersion which we overcome by combining the approach of Coe-Tolomeo (2024) with an iteration argument due to Forlano-Tolomeo (2024) to obtain long-time higher integrability bounds on the transported density.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"26 3","pages":"93"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13518377/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148841602","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":"Existence of variational solutions to doubly nonlinear systems in nondecreasing domains.","authors":"Leah Schätzler, Christoph Scheven, Jarkko Siltakoski, Calvin Stanko","doi":"10.1007/s00028-025-01145-y","DOIUrl":"10.1007/s00028-025-01145-y","url":null,"abstract":"&lt;p&gt;&lt;p&gt;For &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;∞&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; , we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form &lt;dispformula&gt; &lt;math&gt; &lt;mrow&gt; &lt;mtable&gt; &lt;mtr&gt; &lt;mtd&gt; &lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;∂&lt;/mi&gt; &lt;mi&gt;t&lt;/mi&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;/mrow&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mo&gt;div&lt;/mo&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;/mrow&gt; &lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt; &lt;mi&gt;ξ&lt;/mi&gt;&lt;/msub&gt; &lt;mi&gt;f&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;D&lt;/mi&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt; &lt;mi&gt;u&lt;/mi&gt;&lt;/msub&gt; &lt;mi&gt;f&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;D&lt;/mi&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/mtd&gt; &lt;/mtr&gt; &lt;/mtable&gt; &lt;/mrow&gt; &lt;/math&gt; &lt;/dispformula&gt; in a bounded noncylindrical domain &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt; &lt;mo&gt;⊂&lt;/mo&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;/mrow&gt; &lt;/math&gt; . We assume that &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;↦&lt;/mo&gt; &lt;mi&gt;f&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;ξ&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; is integrable, that &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;ξ&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt; &lt;mo&gt;↦&lt;/mo&gt; &lt;mi&gt;f&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;ξ&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; is convex, and that &lt;i&gt;f&lt;/i&gt; satisfies a &lt;i&gt;p&lt;/i&gt;-coercivity condition for some &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;∞&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; . However, we do not impose any specific growth condition from above on &lt;i&gt;f&lt;/i&gt;. For nondecreasing domains that merely satisfy &lt;math&gt; &lt;mrow&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;∂&lt;/mi&gt; &lt;mi&gt;E&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt; &lt;/math&gt; , we prove the existence of variational solutions &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;msup&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mn&gt;0&lt;/mn&gt;&lt;/msup&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;T&lt;/mi&gt; &lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;;&lt;/mo&gt; &lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt; &lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;E&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt; &lt;mi&gt;N&lt;/mi&gt;&lt;/msup&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; via a nonlinear version of the method of minimizing movements. Moreover, under additional assumptions on &lt;i&gt;E&lt;/i&gt; and a &lt;i&gt;p&lt;/i&gt;-growth condition on &lt;i&gt;f&lt;/i&gt;, we show that &lt;math&gt; &lt;mrow&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt; &lt;mi&gt;u&lt;/mi&gt; &lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt; &lt;/math&gt; admits a weak time derivative in the dual &lt;math&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;msup&gt;&lt;mi&gt;V&lt;/mi&gt; &lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;E&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;'&lt;/mo&gt;&lt;/msup&gt; &lt;/math&gt; of the subspace &lt;math&gt; &lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;V&lt;/mi&gt; &lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt; &lt;","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"26 1","pages":"6"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12811320/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145999579","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":"Stability of Minkowski-type inequalities in certain warped product spaces.","authors":"Prachi Sahjwani","doi":"10.1007/s00028-026-01244-4","DOIUrl":"https://doi.org/10.1007/s00028-026-01244-4","url":null,"abstract":"<p><p>This paper proves quantitative stability estimates for five Minkowski-type inequalities for hypersurfaces in warped product spaces. In each case we show that if a hypersurface nearly achieves equality, it must be geometrically close, in the Hausdorff sense, to a radial slice. The ambient spaces are warped products <math> <mrow><mrow><mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo></mrow> <mo>×</mo> <msup><mrow><mi>S</mi></mrow> <mi>n</mi></msup> </mrow> </math> with metric <math><mrow><mtext>d</mtext> <msup><mi>r</mi> <mn>2</mn></msup> <mo>+</mo> <msup><mi>λ</mi> <mn>2</mn></msup> <mrow><mo>(</mo> <mi>r</mi> <mo>)</mo></mrow> <msub><mi>g</mi> <msup><mrow><mi>S</mi></mrow> <mi>n</mi></msup> </msub> </mrow> </math> , as well as the Reissner-Nordström Anti-de Sitter (RN-AdS) and Anti-de Sitter Schwarzschild (AdS-Schwarzschild) manifolds. The proofs combine two ingredients: a quantitative analysis of locally constrained inverse curvature flows, which yields bounds on the traceless second fundamental form in terms of the deficit in the inequality, and a new rigidity theorem for hypersurfaces in locally conformally flat spaces, which converts such bounds into Hausdorff closeness to a radial slice.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"26 4","pages":"100"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13574728/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148978737","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":"Ramifications of generalized Feller theory.","authors":"Christa Cuchiero, Tonio Möllmann, Josef Teichmann","doi":"10.1007/s00028-025-01148-9","DOIUrl":"10.1007/s00028-025-01148-9","url":null,"abstract":"<p><p>Generalized Feller theory provides an important analog to Feller theory beyond locally compact metric state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or infinite-dimensional affine and polynomial processes which appear prominently in the theory of signature stochastic differential equations. We extend several folklore results related to generalized Feller processes, in particular on their construction and path properties, and provide the often quite sophisticated proofs in full detail. We also introduce the new concept of extended Feller processes and compare them with classical and generalized ones as well as with Doob's h-transform. A key example relates generalized Feller semigroups of algebra homomorphisms via the method of characteristics to transport equations and continuous semiflows on weighted spaces, i.e., a remarkably generic way to treat differential equations on weighted spaces. We also provide a counterexample, which shows that no condition of the basic definition of generalized Feller semigroups can be dropped.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"26 1","pages":"8"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12811329/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145999649","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":"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":"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}

{"title":"Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces.","authors":"Wojciech Górny","doi":"10.1007/s00028-025-01071-z","DOIUrl":"https://doi.org/10.1007/s00028-025-01071-z","url":null,"abstract":"<p><p>We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solution to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their existence and uniqueness and show that they are also variational solutions; in particular, this is an existence result for variational solutions. Then, we apply this technique in the case of a gradient flow of a functional with inhomogeneous growth.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 2","pages":"44"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12050237/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144031141","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":"A higher-order quadratic NLS equation on the half-line.","authors":"A Alexandrou Himonas, Fangchi Yan","doi":"10.1007/s00028-024-01034-w","DOIUrl":"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}

{"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}

{"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}