JournalsaihpcVol. 32, No. 1pp. 183–200

A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians

  • Filippo Cagnetti

    Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal

  • Diogo Gomes

    Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, King Abdullah University of Science and Technology (KAUST), CSMSE Division, Thuwal 23955-6900, Saudi Arabia

  • Hiroyoshi Mitake

    Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan

  • Hung V. Tran

    Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA
A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians cover
Download PDF

Abstract

We investigate large-time asymptotics for viscous Hamilton–Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.

Cite this article

Filippo Cagnetti, Diogo Gomes, Hiroyoshi Mitake, Hung V. Tran, A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 183–200

DOI 10.1016/J.ANIHPC.2013.10.005