On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions

DOI10.1007/s00205-011-0484-1zbMath1282.70037arXiv1109.2762OpenAlexW2053814518MaRDI QIDQ2276300

Hiroyoshi Mitake, Hitoshi Ishii, Guy Barles

Publication date: 5 November 2012

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.2762

zbMATH Keywords

convergenceAubry-Mather setCauchy-von Neumann problemweak KAM approach

Mathematics Subject Classification ID

Hamilton-Jacobi equations in mechanics (70H20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) PDEs in connection with mechanics of particles and systems of particles (35Q70)

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Cites Work

• Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions
• Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions
• Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton-Jacobi equations with noncoercive Hamiltonians
• The large-time behavior of solutions of Hamilton-Jacobi equations on the real line
• Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data
• Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE's
• Perron's method for Hamilton-Jacobi equations
• A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation
• Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians
• Neumann type boundary conditions for Hamilton-Jacobi equations
• Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications
• Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations
• Asymptotic solutions of Hamilton-Jacobi equations with state constraints
• Large time behavior of solutions to parabolic equations with Neumann boundary conditions
• Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean \(n\) space
• The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations
• Convergence to Time-Periodic Solutions in Time-Periodic Hamilton–Jacobi Equations on the Circle
• Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space
• A Generalized Dynamical Approach to the Large Time Behavior of Solutions of Hamilton--Jacobi Equations
• Asymptotic Solutions of Hamilton–Jacobi Equations with Semi-Periodic Hamiltonians
• Fully nonlinear Neumann type boundary conditions for first-order Hamilton–Jacobi equations
• User’s guide to viscosity solutions of second order partial differential equations
• Sur la convergence du semi-groupe de Lax-Oleinik
• Remarks on the long time behaviour of the solutions of hamilton-jacobi equations
• On the Large Time Behavior of Solutions of Hamilton--Jacobi Equations
• A PDE Approach to Large-Time Asymptotics for Boundary-Value Problems for Nonconvex Hamilton–Jacobi Equations
• Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations
• Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians
• Ergodic Type Problems and Large Time Behaviour of Unbounded Solutions of Hamilton–Jacobi Equations
• Convergence to steady states or periodic solutions in a class of Hamilton-Jacobi equations

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