Journal of Differential Equations最新文献

{"title":"Transmission problems for simply connected domains in the complex plane","authors":"María J. Carro ,&nbsp;Virginia Naibo ,&nbsp;María Soria-Carro","doi":"10.1016/j.jde.2025.113216","DOIUrl":"10.1016/j.jde.2025.113216","url":null,"abstract":"<div><div>We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower half planes. Our techniques are based on the use of conformal maps and Rellich identities for the Hilbert transform, and are motivated by previous works concerning the Dirichlet, Neumann and Zaremba problems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113216"},"PeriodicalIF":2.4,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609222","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, multiplicity and classification results for solutions to k-Hessian equations with general weights","authors":"João Marcos do Ó ,&nbsp;Justino Sánchez ,&nbsp;Evelina Shamarova","doi":"10.1016/j.jde.2025.02.085","DOIUrl":"10.1016/j.jde.2025.02.085","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The present paper is concerned with negative classical solutions to a &lt;em&gt;k&lt;/em&gt;-Hessian equation involving a nonlinearity with a general weight&lt;span&gt;&lt;span&gt;&lt;span&gt;(&lt;em&gt;P&lt;/em&gt;)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&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;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;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;in &lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;on &lt;/mtext&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; Here, &lt;em&gt;B&lt;/em&gt; denotes the unit ball in &lt;span&gt;&lt;math&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;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;λ&lt;/em&gt; is a positive parameter and &lt;span&gt;&lt;math&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The function &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; satisfies very general conditions in the radial direction &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. We show the existence, nonexistence, and multiplicity of solutions to Problem &lt;span&gt;&lt;span&gt;(&lt;em&gt;P&lt;/em&gt;)&lt;/span&gt;&lt;/span&gt;. The main technique used for the proofs is a phase-plane analysis related to a non-autonomous dynamical system associated to the equation in &lt;span&gt;&lt;span&gt;(&lt;em&gt;P&lt;/em&gt;)&lt;/span&gt;&lt;/span&gt;. Further, using the aforementioned non-autonomous system, we give a comprehensive characterization of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-, &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-, &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-solutions to the related problem&lt;span&gt;&lt;span&gt;&lt;span&gt;(&lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt;)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; given on the entire space &lt;span&gt;&lt;math&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;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/spa","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113214"},"PeriodicalIF":2.4,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610349","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":"Global well-posedness for the hydrostatic Oldroyd-B model","authors":"Marius Paicu ,&nbsp;Tianyuan Yu ,&nbsp;Ning Zhu","doi":"10.1016/j.jde.2025.113224","DOIUrl":"10.1016/j.jde.2025.113224","url":null,"abstract":"<div><div>The Oldroyd-B model plays an important role in the viscoelastic flows. In this paper, we study the Oldroyd-B model in a strip domain <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>. We first derive the hydrostatic approximate system for the Oldroyd-B model and then we prove the global well-posedness of this limit system with small analytic data in horizontal variable. Finally, we justify the limit from the re-scaled Oldroyd-B model to the hydrostatic Oldroyd-B model.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113224"},"PeriodicalIF":2.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601427","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":"Partial regularity for degenerate systems of double phase type","authors":"Jihoon Ok ,&nbsp;Giovanni Scilla ,&nbsp;Bianca Stroffolini","doi":"10.1016/j.jde.2025.02.078","DOIUrl":"10.1016/j.jde.2025.02.078","url":null,"abstract":"<div><div>We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by <span><math><mi>H</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>+</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mi>t</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> with <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mi>q</mi></math></span> and <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> a nonnegative <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-continuous function. Our main result proves that if <span><math><mfrac><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></mfrac><mo>≤</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mi>n</mi></mrow></mfrac></math></span>, the gradient of any weak solution is locally Hölder continuous, except on a set of measure zero.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113207"},"PeriodicalIF":2.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577574","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":"From local to global dynamics in Kolmogorov polynomial vector fields","authors":"Hongjin He ,&nbsp;Dongmei Xiao","doi":"10.1016/j.jde.2025.02.083","DOIUrl":"10.1016/j.jde.2025.02.083","url":null,"abstract":"<div><div>In this paper we provide an approach to characterize global dynamics from local linearized dynamics of Kolmogorov polynomial vector fields, and establish a link between the integrability of the vector field and the intersection number of the corresponding algebraic curves. Specially, a new criterion on nonexistence of limit cycles is given for Kolmogorov polynomial vector fields with any degree <em>n</em>. As an application of the results, we consider Kolmogorov quadratic and cubic polynomial vector fields, whose number of either center-type equilibria or weak saddles reaches the maximum in the interior of quadrants of real plane denoted by Int<span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and obtain all topological classifications of their global dynamics in Poincaré disc by index theory and qualitative analysis. Notably, it is shown that the local dynamics of Kolmogorov quadratic polynomial vector fields (weakly nonlinear) having a center-type equilibrium or a weak saddle in Int<span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> can completely determine its global dynamics in Poincaré disc, but the local dynamics of Kolmogorov cubic polynomial vector fields (strongly nonlinear) having four center-type equilibria or four weak saddles in Int<span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> cannot completely determine its global dynamics in Poincaré disc.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113212"},"PeriodicalIF":2.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577976","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":"Similarity between two distributed parameter systems","authors":"Xiaoying Wang ,&nbsp;Yong Li ,&nbsp;Shuguan Ji","doi":"10.1016/j.jde.2025.113218","DOIUrl":"10.1016/j.jde.2025.113218","url":null,"abstract":"<div><div>The relationship between two distributed parameter systems can be linked by a homeomorphic mapping, and the core is to study the minimizer of the functional to measure the degree of their similarity. We prove the existence and the necessary conditions (a maximum principle) for the minimizer. The similarity degree between two distributed parameter systems is thus defined by the functional, which extends the conjugacy in dynamical systems. As applications, we consider parabolic systems that satisfy different similarities. We prove a Hartman-Grobman theorem for general parabolic systems. We also demonstrate asymptotic similarity for the general quasilinear parabolic systems, indicating the Clausius statement of the second law of thermodynamics.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113218"},"PeriodicalIF":2.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577572","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":"Singularity analysis of a semilinear Bernoulli-type free boundary problem near the stagnation point","authors":"Yang Pu","doi":"10.1016/j.jde.2025.02.079","DOIUrl":"10.1016/j.jde.2025.02.079","url":null,"abstract":"<div><div>This study presents a thorough singularity analysis of Bernoulli-type free boundary problem for semilinear elliptic equation, with a particular emphasis on the asymptotic behavior near stagnation points where the gradient of solution vanishes. The findings, derived from variational and weak solutions, rely on the monotonicity formula to construct the blow-up limit, thereby identifying that the possible singular profiles near stagnation points are constrained to corner, cusp, or flat singularity. Additionally, the application of frequency formula eliminates the possibility of flat singularity. Through a further symbol limitation at the right hand side of equation, we show that cusp singularity is impossible. The only admissible singular profile is a corner, whose angle depends on the decay rate of the solution near the stagnation point.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113208"},"PeriodicalIF":2.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577573","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":"Wong-Zakai approximations and support theorem for reflected SDEs with path-dependent coefficients","authors":"Jiagang Ren ,&nbsp;Sheng Wang ,&nbsp;Jing Wu","doi":"10.1016/j.jde.2025.113219","DOIUrl":"10.1016/j.jde.2025.113219","url":null,"abstract":"<div><div>In this paper we establish the Wong-Zakai approximation result for reflected stochastic differential equations (SDEs) with path-dependent coefficients. Based on the newly established limit theorem, we also establish the support theorem for the solution process of this type of equations, which is accomplished through the non-anticipative functional calculus.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113219"},"PeriodicalIF":2.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577978","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":"Global and exponential attractors for a suspension bridge model with nonlinear damping","authors":"L.G.R. Miranda ,&nbsp;C.A. Raposo ,&nbsp;M.M. Freitas","doi":"10.1016/j.jde.2025.113217","DOIUrl":"10.1016/j.jde.2025.113217","url":null,"abstract":"<div><div>In this manuscript, for the first time in the literature, we study the asymptotic analysis of compact global attractors of oscillations in suspension bridges, modeled by the Timoshenko Theory. Instead of showing the existence of an absorbing set, we prove the system is gradient and asymptotically smooth and hence obtain the existence of a global attractor, characterized as an unstable manifold of the set of stationary solutions. We use the recent quasi-stability theory developed by Chueshov and Lasiecka <span><span>[4]</span></span>, <span><span>[5]</span></span> directly on a bounded positively invariant set to prove the smoothness and finite fractal dimension of the attractor, as well as the existence of exponential attractors and determining functionals.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113217"},"PeriodicalIF":2.4,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578148","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":"Global existence for the semilinear regular Euler-Poisson-Darboux-Tricomi equation","authors":"Yuequn Li ,&nbsp;Fei Guo","doi":"10.1016/j.jde.2025.02.082","DOIUrl":"10.1016/j.jde.2025.02.082","url":null,"abstract":"<div><div>For the semilinear Euler-Poisson-Darboux-Tricomi equation with a power nonlinearity, we derive that if the damping term dominates over the mass term, the small initial data solution exists globally if <span><math><mi>p</mi><mo>&gt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>(</mo><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mi>μ</mi><mo>−</mo><mn>1</mn><mo>−</mo><msqrt><mrow><mi>δ</mi></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></math></span>. Combining with the blow-up results established by Palmieri <span><span>[26]</span></span> recently, we claim that <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>(</mo><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mi>μ</mi><mo>−</mo><mn>1</mn><mo>−</mo><msqrt><mrow><mi>δ</mi></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></math></span> is indeed the critical exponent for the equation in this case. Here, <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>(</mo><mi>l</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>l</mi></mrow></mfrac></math></span> is the well-known Fujita index.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113211"},"PeriodicalIF":2.4,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577979","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}