Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 150, Issue 3, Pages 1187-1196Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15736
Keywords
Hamilton-Jacobi equations; viscosity solutions; finite-time convergence; weak KAM theory
Categories
Funding
- NSFC [12171096, 11790273, 12171315, 11931016]
- Innovation Program of Shanghai Municipal Education Commission [2021-01-07-00-02-E00087]
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This paper deals with the long-time behavior of viscosity solutions of evolutionary contact Hamilton-Jacobi equations. It shows the connection between viscosity solutions of the ergodic contact Hamilton-Jacobi equation and solutions of the evolutionary equation.
This paper deals with the long-time behavior of viscosity solutions of evolutionary contact Hamilton-Jacobi equations w(t) + H(x, w, w(x)) = 0, where H(x, u, p) is strictly decreasing in u and satisfies Tonelli conditions in p. We show that each viscosity solution of the ergodic contact Hamilton-Jacobi equation H(x, u, u(x)) = 0 can be reached by many different viscosity solutions of the above evolutionary equation in a finite time.
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