Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Singular elliptic measure data problems with irregular obstacles","authors":"Sun-Sig Byun ,&nbsp;Kyeong Song ,&nbsp;Yeonghun Youn","doi":"10.1016/j.na.2024.113559","DOIUrl":"https://doi.org/10.1016/j.na.2024.113559","url":null,"abstract":"<div><p>We investigate elliptic irregular obstacle problems with <span><math><mi>p</mi></math></span>-growth involving measure data. Emphasis is on the strongly singular case <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>n</mi></mrow></math></span>, and we obtain several new comparison estimates to prove gradient potential estimates in an intrinsic form. Our approach can be also applied to derive zero-order potential estimates.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140894453","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":"An upper bound for the box dimension of the hyperbolic dynamics via unstable topological pressure","authors":"Congcong Qu","doi":"10.1016/j.na.2024.113560","DOIUrl":"https://doi.org/10.1016/j.na.2024.113560","url":null,"abstract":"<div><p>In this paper, we utilize the sub-additive unstable topological pressure to give an upper bound for the upper box dimension of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> hyperbolic set on local unstable manifold. As a by-product, we give a new expression of the topological pressure on symbolic spaces. This work is inspired by Barreira (1996), Feng and Simon (2023) and Zhang et al. (2022).</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140893739","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":"Convex hull property for elliptic and parabolic systems of PDE","authors":"Antonín Češík","doi":"10.1016/j.na.2024.113554","DOIUrl":"https://doi.org/10.1016/j.na.2024.113554","url":null,"abstract":"<div><p>We study the convex hull property for systems of partial differential equations. This is a generalization of the maximum principle for a single equation. We show that the convex hull property holds for a class of elliptic and parabolic systems of non-linear partial differential equations. In particular, this includes the case of the parabolic <span><math><mi>p</mi></math></span>-Laplace system. The coupling conditions for coefficients are demonstrated to be optimal by means of respective counterexamples.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140815577","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":"Precise rates of propagation in reaction–diffusion equations with logarithmic Allee effect","authors":"Emeric Bouin ,&nbsp;Jérôme Coville ,&nbsp;Xi Zhang","doi":"10.1016/j.na.2024.113557","DOIUrl":"https://doi.org/10.1016/j.na.2024.113557","url":null,"abstract":"<div><p>This paper focuses on propagation phenomena in reaction–diffusion equations with a weakly degenerate monostable nonlinearity. The kind of reaction term we consider can be seen as an intermediate between the classical logistic one (or Fisher–KPP) and more usual power laws that usually model Allee effects. We investigate the effect of the decay rate of the initial data on the propagation rate. When the tail of the initial data is sub-exponential, both finite speed propagation and acceleration may happen. We derive the exact separation between the two situations. When the initial data is sub-exponentially unbounded, acceleration unconditionally occurs. Estimates for the locations of the level sets are expressed in terms of the decay of the initial data. In addition, sharp exponents of acceleration for initial data with sub-exponential and algebraic tails are given. Numerical simulations are presented to illustrate the above findings.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140816174","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 very singular solution for the Anisotropic Fast Diffusion Equation and its consequences","authors":"Juan Luis Vázquez","doi":"10.1016/j.na.2024.113556","DOIUrl":"https://doi.org/10.1016/j.na.2024.113556","url":null,"abstract":"<div><p>We construct the Very Singular Solution (VSS) for the Anisotropic Fast Diffusion Equation (AFDE) in the suitably good exponent range. VSS is a solution that, starting from an infinite mass located at one point as initial datum, evolves as an admissible solution of the corresponding equation everywhere away from the point singularity. It is expected to represent important properties of the fundamental solutions when the initial mass is very big. Here we work in the whole Euclidean space.</p><p>In this setting we show how the diffusion process distributes mass from the initial infinite singularity with different rates along the different space directions. Indeed, and up to constant factors, there is a simple partition formula for the anisotropic mass expansion, given approximately as the minimum of separate 1-D VSS solutions. This striking fact is a consequence of the improved scaling properties of the special solution, and it has strong consequences.</p><p>If we consider the family of fundamental solutions for different masses, we prove that they all share the same universal tail behaviour (i.e., for large <span><math><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></math></span>) as the VSS. Namely, their tail is asymptotically convergent to the unique VSS tail. This means that the VSS partition formula holds also for the fundamental solutions at spatial infinity. With the help of this analysis we study the behaviour of the class of nonnegative finite-mass solutions of the Anisotropic FDE, and prove the Global Harnack Principle (GHP) and the Asymptotic Convergence in Relative Error (ACRE) under a natural assumption on the decay of the initial tail.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24000750/pdfft?md5=3099aa83cf073382403f0935a66d729a&pid=1-s2.0-S0362546X24000750-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140650763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a new singular and degenerate extension of the p-Laplace operator","authors":"George Baravdish ,&nbsp;Yuanji Cheng ,&nbsp;Olof Svensson","doi":"10.1016/j.na.2024.113553","DOIUrl":"https://doi.org/10.1016/j.na.2024.113553","url":null,"abstract":"<div><p>We study a novel degenerate and singular elliptic operator <span><math><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mrow><mo>(</mo><mi>τ</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow></mrow></msub></math></span> defined by <span><math><mrow><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mrow><mo>(</mo><mi>τ</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow></mrow></msub><mi>u</mi><mo>=</mo><mi>τ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>u</mi><mo>+</mo><mi>χ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>)</mo></mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>∞</mi></mrow></msub><mi>u</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> where the singular weights <span><math><mrow><mi>τ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>χ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math></span> are continuous functions on <span><math><mrow><mi>Ω</mi><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span>. The operator <span><math><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mrow><mo>(</mo><mi>τ</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow></mrow></msub></math></span> is an extension of <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></mrow></msub><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi></mrow></msup><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>u</mi><mo>+</mo><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><msub><mrow><mi>Δ</mi></mrow><mrow><mi>∞</mi></mrow></msub><mi>u</mi><mo>,</mo><mspace></mspace><mi>p</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mspace></mspace><mi>q</mi><mo>≥</mo><mn>0</mn><mo>,</mo></mrow></math></span> introduced by the authors in Baravdishet al. (2020), which in turn is an extension of the <span><math><mi>p</mi></math></span>-Laplace operator <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>.</mo></mrow></math></span> We establish the well-posedness of the Neumann boundary value problem for the parabolic equation <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mrow><mo>(</mo><mi>τ</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow></mrow></msub><mi>u</mi></mrow></math></span> in the framew","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24000725/pdfft?md5=6ea663f7ef82d1217c13c05825c4031b&pid=1-s2.0-S0362546X24000725-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140639282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Liouville theorems and Harnack inequalities for Allen–Cahn type equation","authors":"Zhihao Lu","doi":"10.1016/j.na.2024.113552","DOIUrl":"https://doi.org/10.1016/j.na.2024.113552","url":null,"abstract":"<div><p>We first give a logarithmic gradient estimate for the local positive solutions of Allen–Cahn equation on the complete Riemannian manifolds with Ricci curvature bounded below. As its natural corollary, Harnack inequality and a Liouville theorem for classical positive solutions are obtained. Later, we consider similar estimate under integral curvature condition and generalize previous results to a class nonlinear equations which contain some classical elliptic equations such as Lane–Emden equation, static Whitehead–Newell equation and static Fisher–KPP equation. Last, we briefly generalize them to equation with gradient item under Bakry–Émery curvature condition.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140618800","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 linearized partial data Calderón problem for Biharmonic operators","authors":"Divyansh Agrawal ,&nbsp;Ravi Shankar Jaiswal ,&nbsp;Suman Kumar Sahoo","doi":"10.1016/j.na.2024.113544","DOIUrl":"https://doi.org/10.1016/j.na.2024.113544","url":null,"abstract":"<div><p>We consider a linearized partial data Calderón problem for biharmonic operators extending the analogous result for harmonic operators (Dos Santos Ferreira et al., 2009). We construct special solutions and utilize Segal-Bargmann transform to recover lower order perturbations.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140618799","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":"Corrigendum to ‘Applications of Strassen’s theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions’ [Nonlinear Anal., 232 (2023) 113267]","authors":"Krzysztof J. Ciosmak","doi":"10.1016/j.na.2024.113542","DOIUrl":"https://doi.org/10.1016/j.na.2024.113542","url":null,"abstract":"<div><p>In Ciosmak (2023), Theorem 2.3. does not suffice for its applications. We strengthen Theorem 2.1. and Theorem 2.3., so that they imply their claimed consequences. Moreover, we correct a minor flaw in the proof of Proposition 2.4.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24000610/pdfft?md5=294c3696606f0cc6445a9566aa4f046d&pid=1-s2.0-S0362546X24000610-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140549225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic behavior of the 3D incompressible Navier–Stokes equations with damping","authors":"Fuxian Peng ,&nbsp;Xueting Jin ,&nbsp;Huan Yu","doi":"10.1016/j.na.2024.113543","DOIUrl":"https://doi.org/10.1016/j.na.2024.113543","url":null,"abstract":"<div><p>In this paper, we consider the 3D incompressible Navier–Stokes equations with damping term <span><math><mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>β</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mrow><mo>(</mo><mi>β</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow><mo>.</mo></mrow></math></span> First, by using a different and simple method from Cai and Lei (2010), Jia et al. (2011), Jiang (2012) and Yu and Zheng (2019), for any <span><math><mrow><mi>β</mi><mo>≥</mo><mn>1</mn><mo>,</mo></mrow></math></span> we prove that the weak solutions decay to zero in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> as time tends to infinity; for any <span><math><mrow><mi>β</mi><mo>≥</mo><mn>3</mn><mo>,</mo></mrow></math></span> we derive optimal decay rates of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm of the solutions. Second, we obtain the decay rate with some appropriate space weighted estimates, which is the first result on the 3D damped Navier–Stokes equations to our knowledge.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140549224","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}