Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Stable s-minimal cones in R2 are flat for s∼0","authors":"Michele Caselli","doi":"10.1016/j.na.2025.113828","DOIUrl":"10.1016/j.na.2025.113828","url":null,"abstract":"<div><div>For <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> small, we show that the only cones in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stationary for the <span><math><mi>s</mi></math></span>-perimeter and stable in <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> are half-planes. This is in direct contrast with the case of the classical perimeter or the regime <span><math><mi>s</mi></math></span> close to 1, where nontrivial cones as <span><math><mrow><mrow><mo>{</mo><mi>x</mi><mi>y</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></mrow><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> are stable for inner variations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113828"},"PeriodicalIF":1.3,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143890946","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 a finite-volume scheme for a stochastic Allen–Cahn problem with constraint","authors":"Caroline Bauzet ,&nbsp;Cédric Sultan ,&nbsp;Guy Vallet ,&nbsp;Aleksandra Zimmermann","doi":"10.1016/j.na.2025.113812","DOIUrl":"10.1016/j.na.2025.113812","url":null,"abstract":"<div><div>The aim of this contribution is to address the convergence study of a time and space approximation scheme for an Allen–Cahn problem with constraint and perturbed by a multiplicative noise of Itô type. The problem is set in a bounded domain of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> (with <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span> or 3) and homogeneous Neumann boundary conditions are considered. The employed strategy consists in building a numerical scheme on a regularized version “à la Moreau-Yosida” of the constrained problem, and passing to the limit simultaneously with respect to the regularization parameter and the time and space steps, denoted respectively by <span><math><mi>ϵ</mi></math></span>, <span><math><mrow><mi>Δ</mi><mi>t</mi></mrow></math></span> and <span><math><mi>h</mi></math></span>. Combining a semi-implicit Euler–Maruyama time discretization with a Two-Point Flux Approximation (TPFA) scheme for the spatial variable, one is able to prove, under the assumption <span><math><mrow><mi>Δ</mi><mi>t</mi><mo>=</mo><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn><mo>+</mo><mi>θ</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> for a positive <span><math><mi>θ</mi></math></span>, the convergence of such a “<span><math><mrow><mo>(</mo><mi>ϵ</mi><mo>,</mo><mi>Δ</mi><mi>t</mi><mo>,</mo><mi>h</mi><mo>)</mo></mrow></math></span>” scheme towards the unique weak solution of the initial problem, <em>a priori</em> strongly in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>Λ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> and <em>a posteriori</em> also strongly in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>×</mo><mi>Λ</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> for any finite <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113812"},"PeriodicalIF":1.3,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888024","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":"Scattering for the one dimensional Hartree Fock equation","authors":"Cyril Malézé","doi":"10.1016/j.na.2025.113834","DOIUrl":"10.1016/j.na.2025.113834","url":null,"abstract":"<div><div>We consider the Hartree–Fock equation in 1D, for a small and localised initial data and a finite measure potential. We show that there is no long range scattering due to a nonlinear cancellation between the direct term and the exchange term for plane waves. We employ the framework of space–time resonances that enables us to single out precisely this cancellation and to obtain scattering to linear waves as a consequence.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113834"},"PeriodicalIF":1.3,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881722","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":"Convergence of first-order quasilinear hyperbolic systems to hyperbolic-parabolic systems","authors":"Yue-Jun Peng ,&nbsp;Shuimiao Du","doi":"10.1016/j.na.2025.113830","DOIUrl":"10.1016/j.na.2025.113830","url":null,"abstract":"<div><div>We provide a framework to study the zero relaxation time limit of Cauchy problem for first-order quasilinear hyperbolic systems with relaxation in several space dimensions. For this purpose, we construct an approximate solution by a formal asymptotic expansion with initial layer corrections. The system of the leading term in the expansion is governed by a hyperbolic-parabolic system. Under appropriate structural and partial dissipation conditions, we justify rigorously the validity of the asymptotic expansion on a time interval independent of the relaxation time, provided that the system of the leading term admits a local-in-time smooth solution. The main theorem of the present paper includes the results obtained in previous works and applies to additional examples of models arising in fluid mechanics.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113830"},"PeriodicalIF":1.3,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888025","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":"Gradient integrability estimates for elliptic double-obstacle problems with degenerate matrix weights","authors":"Minh-Phuong Tran ,&nbsp;Thanh-Nhan Nguyen","doi":"10.1016/j.na.2025.113833","DOIUrl":"10.1016/j.na.2025.113833","url":null,"abstract":"<div><div>The main objective of this paper is to study a regularity estimate for solutions to a certain elliptic double-obstacle problem involving <span><math><mi>p</mi></math></span>-Laplacian with degenerate weights. Motivated by the recent advances in this topic, we derive a general decay estimate for level sets of solutions’ gradients, toward understanding the regularity properties of obstacle problems involving a matrix-valued weight. In turn, it allows us to establish global norm estimates in a variety of specific families of spaces.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113833"},"PeriodicalIF":1.3,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143887515","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":"Fast reaction limit for a Leslie–Gower model including preys, meso-predators and top-predators","authors":"L. Desvillettes ,&nbsp;L. Fiorentino ,&nbsp;T. Mautone","doi":"10.1016/j.na.2025.113817","DOIUrl":"10.1016/j.na.2025.113817","url":null,"abstract":"<div><div>We consider a system of three reaction–diffusion equations modeling the interaction between a prey species and two predators species including functional responses of Holly type-II and Leslie–Gower type. We propose a reaction–diffusion model with five equations with simpler functional responses which, in the fast reaction limit, allows to recover the zero-th order terms of the initially considered system. The diffusive part of the initial equations is however modified and cross diffusion terms pop up. We first study the equilibria of this new system and show that no Turing instability appears. We then rigorously prove a partial result of convergence for the fast reaction limit (in 1D and 2D).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113817"},"PeriodicalIF":1.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874392","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":"Formation and construction of shock for p-system under degenerate conditions of finite or infinite orders","authors":"Jintao Li ,&nbsp;Lu Zhu","doi":"10.1016/j.na.2025.113824","DOIUrl":"10.1016/j.na.2025.113824","url":null,"abstract":"<div><div>In this paper, we are concerned with the shock formation and construction for <span><math><mi>p</mi></math></span>-system when the initial data are degenerate with finite or infinite orders (see <span><span>(1.6)</span></span> or <span><span>(1.7)</span></span> below). Since the solution we consider is a simple wave before shock formation, then with the help of the construction of shock solutions for the corresponding scalar equation, we establish the detailed estimates of the approximate solutions and then prove the convergence of the approximate solutions. Thus a weak entropy solution and a shock curve starting from the blowup point are constructed under two types of degenerate conditions. Meanwhile, some precise descriptions on the behaviors of the solutions near the blowup point are given.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113824"},"PeriodicalIF":1.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868927","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":"A curvature flow approach to the Lp chord Minkowski problem","authors":"Manli Cheng ,&nbsp;Lan Tang","doi":"10.1016/j.na.2025.113825","DOIUrl":"10.1016/j.na.2025.113825","url":null,"abstract":"<div><div>In this work, we mainly consider the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> chord Minkowski problem and the existence results of solutions to this problem have been established by the method of flow governed by parabolic equations for the two cases: (1) <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mi>n</mi><mo>+</mo><mi>q</mi><mo>−</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span>; (2) <span><math><mrow><mi>p</mi><mo>&gt;</mo><mi>n</mi></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span> .</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113825"},"PeriodicalIF":1.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869049","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":"New atomic decompositions of weighted local Hardy spaces","authors":"Haijing Zhao,&nbsp;Xuechun Yang,&nbsp;Baode Li","doi":"10.1016/j.na.2025.113815","DOIUrl":"10.1016/j.na.2025.113815","url":null,"abstract":"<div><div>We introduce a new class of weighted local approximate atoms including classical weighted local atoms. Then we further obtain the weighted local approximate atomic decompositions of weighted local Hardy spaces <span><math><mrow><msubsup><mrow><mi>h</mi></mrow><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>1</mn></mrow></math></span> and weight <span><math><mrow><mi>ω</mi><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. As an application, we prove the boundedness of inhomogeneous Calderón–Zygmund operators on <span><math><mrow><msubsup><mrow><mi>h</mi></mrow><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> via weighted local approximate atoms and molecules.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113815"},"PeriodicalIF":1.3,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850288","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":"Behaviour at infinity for solutions of a mixed nonlinear elliptic boundary value problem via inversion","authors":"Jana Björn ,&nbsp;Abubakar Mwasa","doi":"10.1016/j.na.2025.113816","DOIUrl":"10.1016/j.na.2025.113816","url":null,"abstract":"<div><div>We study a mixed boundary value problem for the quasilinear elliptic equation <span><math><mrow><mo>div</mo><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mo>∇</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and zero conormal derivative on the rest. The equation is assumed to satisfy the standard ellipticity conditions with a parameter <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. We prove the existence and uniqueness of bounded weak solutions to the mixed problem and characterize the regularity of the point at infinity in terms of <span><math><mi>p</mi></math></span>-capacities. For solutions with only Neumann data near the point at infinity we show that they behave in exactly one of three possible ways, similar to the alternatives in the Phragmén–Lindelöf principle.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113816"},"PeriodicalIF":1.3,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848384","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}