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Annales De L Institut Henri Poincare-Analyse Non Lineaire最新文献

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Traveling waves for a nonlocal KPP equation and mean-field game models of knowledge diffusion 非局部KPP方程的行波及知识扩散的平均场博弈模型
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-10-21 DOI: 10.4171/aihpc/26
A. Porretta, L. Rossi
{"title":"Traveling waves for a nonlocal KPP equation and mean-field game models of knowledge diffusion","authors":"A. Porretta, L. Rossi","doi":"10.4171/aihpc/26","DOIUrl":"https://doi.org/10.4171/aihpc/26","url":null,"abstract":"We analyze a mean-field game model proposed by economists R.E. Lucas and B. Moll (2014) to describe economic systems where production is based on knowledge growth and diffusion. This model reduces to a PDE system where a backward Hamilton-Jacobi-Bellman equation is coupled with a forward KPP-type equation with nonlocal reaction term. We study the existence of traveling waves for this mean-field game system, obtaining the existence of both critical and supercritical waves. In particular we prove a conjecture raised by economists on the existence of a critical balanced growth path for the described economy, supposed to be the expected stable growth in the long run. We also provide nonexistence results which clarify the role of parameters in the economic model.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"29 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86798714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 4
Existence of solutions for a higher-order semilinear parabolic equation with singular initial data 一类具有奇异初始数据的高阶半线性抛物方程解的存在性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-09-01 DOI: 10.1016/j.anihpc.2020.04.002
Kazuhiro Ishige , Tatsuki Kawakami , Shinya Okabe
{"title":"Existence of solutions for a higher-order semilinear parabolic equation with singular initial data","authors":"Kazuhiro Ishige ,&nbsp;Tatsuki Kawakami ,&nbsp;Shinya Okabe","doi":"10.1016/j.anihpc.2020.04.002","DOIUrl":"10.1016/j.anihpc.2020.04.002","url":null,"abstract":"<div><p>We establish the existence of solutions of the Cauchy problem for a higher-order semilinear<span> parabolic equation<span> by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.</span></span></p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"37 5","pages":"Pages 1185-1209"},"PeriodicalIF":1.9,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.04.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82409217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 13
New concentration phenomena for a class of radial fully nonlinear equations 一类径向全非线性方程的新的集中现象
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-09-01 DOI: 10.1016/j.anihpc.2020.03.003
Giulio Galise , Alessandro Iacopetti , Fabiana Leoni , Filomena Pacella
{"title":"New concentration phenomena for a class of radial fully nonlinear equations","authors":"Giulio Galise ,&nbsp;Alessandro Iacopetti ,&nbsp;Fabiana Leoni ,&nbsp;Filomena Pacella","doi":"10.1016/j.anihpc.2020.03.003","DOIUrl":"10.1016/j.anihpc.2020.03.003","url":null,"abstract":"<div><p><span><span>We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems<span> in a ball, driven by the extremal<span> Pucci's operators and with a power nonlinear term. We first determine a new </span></span></span>critical exponent<span><span> related to the existence or nonexistence of such solutions. Then we analyze the </span>asymptotic behavior of the radial </span></span>nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value.</p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"37 5","pages":"Pages 1109-1141"},"PeriodicalIF":1.9,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.03.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72529841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 1
The Calderón problem for quasilinear elliptic equations 拟线性椭圆方程的Calderón问题
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-09-01 DOI: 10.1016/j.anihpc.2020.03.004
Claudio Muñoz , Gunther Uhlmann
{"title":"The Calderón problem for quasilinear elliptic equations","authors":"Claudio Muñoz ,&nbsp;Gunther Uhlmann","doi":"10.1016/j.anihpc.2020.03.004","DOIUrl":"10.1016/j.anihpc.2020.03.004","url":null,"abstract":"<div><p>In this paper we show uniqueness of the conductivity for the quasilinear Calderón's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induce a unique Dirichlet-to-Neumann (DN) map. The method of proof considers some complex-valued, linear test functions based on a point of the boundary of the domain, and a linearization of the DN map placed at these particular set of solutions.</p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"37 5","pages":"Pages 1143-1166"},"PeriodicalIF":1.9,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.03.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84518994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 37
Effective viscosity of random suspensions without uniform separation 无均匀分离的随机悬浮液的有效粘度
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-08-30 DOI: 10.4171/aihpc/25
Mitia Duerinckx
{"title":"Effective viscosity of random suspensions without uniform separation","authors":"Mitia Duerinckx","doi":"10.4171/aihpc/25","DOIUrl":"https://doi.org/10.4171/aihpc/25","url":null,"abstract":"This work is devoted to the definition and the analysis of the effective viscosity associated with a random suspension of small rigid particles in a steady Stokes fluid. While previous works on the topic have been conveniently assuming that particles are uniformly separated, we show how some ideas due to Jikov can be adapted to relax this unphysical assumption, in particular allowing for contacts in dimension $d>3$ and for \"almost\" contacts in dimension $d=3$, provided that some geometric non-degeneracy condition is satisfied.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"39 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77137984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 14
A Bernstein-type theorem for minimal graphs over convex domains 凸域上极小图的一个bernstein型定理
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-08-16 DOI: 10.4171/aihpc/18
Nick Edelen, Zhehui Wang
{"title":"A Bernstein-type theorem for minimal graphs over convex domains","authors":"Nick Edelen, Zhehui Wang","doi":"10.4171/aihpc/18","DOIUrl":"https://doi.org/10.4171/aihpc/18","url":null,"abstract":"Given any n ≥ 2, we show that if Ω ( Rn is an open convex domain (e.g. a half-space), and u : Ω → R is a solution to the minimal surface equation which agrees with a linear function on ∂Ω, then u must itself be linear.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81652789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 2
High degeneracy of effective Hamiltonian in two dimensions 二维有效哈密顿量的高简并性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-08-08 DOI: 10.4171/aihpc/6
Yifeng Yu
{"title":"High degeneracy of effective Hamiltonian in two dimensions","authors":"Yifeng Yu","doi":"10.4171/aihpc/6","DOIUrl":"https://doi.org/10.4171/aihpc/6","url":null,"abstract":"Consider the effective Hamiltonian $overline H(p)$ associated with the mechanical Hamiltonian $H(p,x)={1over 2}|p|^2+V(x)$. We prove that for generic $V$, $overline H$ is piecewise 1d in a dense open set in two dimensions using Aubry-Mather theory.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"157 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86728004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The Aronson–Bénilan estimate in Lebesgue spaces 勒贝格空间中的aronson - b<s:1>尼兰估计
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-07-30 DOI: 10.4171/aihpc/43
G. Bevilacqua, B. Perthame, M. Schmidtchen
{"title":"The Aronson–Bénilan estimate in Lebesgue spaces","authors":"G. Bevilacqua, B. Perthame, M. Schmidtchen","doi":"10.4171/aihpc/43","DOIUrl":"https://doi.org/10.4171/aihpc/43","url":null,"abstract":"In a celebrated three-pages long paper in 1979, Aronson and Benilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and Benilan estimate in L p spaces, of some modifications and improvements, as well as to show certain limitations of their strategy.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"120 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88110862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 8
Reaction–diffusion equations in the half-space 半空间中的反应扩散方程
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-07-27 DOI: 10.4171/aihpc/27
H. Berestycki, Cole Graham
{"title":"Reaction–diffusion equations in the half-space","authors":"H. Berestycki, Cole Graham","doi":"10.4171/aihpc/27","DOIUrl":"https://doi.org/10.4171/aihpc/27","url":null,"abstract":"We study reaction-diffusion equations of various types in the half-space. For bistable reactions with Dirichlet boundary conditions, we prove conditional uniqueness: there is a unique nonzero bounded steady state which exceeds the bistable threshold on large balls. Moreover, solutions starting from sufficiently large initial data converge to this steady state as $t to infty$. For compactly supported initial data, the asymptotic speed of this propagation agrees with the unique speed $c_*$ of the one-dimensional traveling wave. We furthermore construct a traveling wave in the half-plane of speed $c_*$. \u0000In parallel, we show analogous results for ignition reactions under both Dirichlet and Robin boundary conditions. Using our ignition construction, we obtain stronger results for monostable reactions with the same boundary conditions. For such reactions, we show in general that there is a unique nonzero bounded steady state. Furthermore, monostable reactions exhibit the hair-trigger effect: every solution with nontrivial initial data converges to this steady state as $t to infty$. Given compactly supported initial data, this disturbance propagates at a speed $c_*$ equal to the minimal speed of one-dimensional traveling waves. We also construct monostable traveling waves in the Dirichlet or Robin half-plane with any speed $c geq c_*$.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"82 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86698567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 1
Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems 齐次线性和拟线性双曲型系统的Lyapunov函数与最优时间有限时间镇定
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2020-07-07 DOI: 10.4171/aihpc/30
J. Coron, Hoai-Minh Nguyen
{"title":"Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems","authors":"J. Coron, Hoai-Minh Nguyen","doi":"10.4171/aihpc/30","DOIUrl":"https://doi.org/10.4171/aihpc/30","url":null,"abstract":"Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous linear and quasilinear hyperbolic systems. In this work, we present Lyapunov's functions for these feedbacks and use estimates for Lyapunov's functions to rediscover the finite stabilization results.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"91 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73704779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 7
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