Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions

Details Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions

2010-08-24

arxiv.org/abs/1008.4028v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

We study the long-time asymptotic behavior of solutions u of the
Hamilton-Jacobi equation u_t(x,t)+H(x,Du(x,t))=0 in \Omega \times (0,\infty),
where \Omega is a bounded open subset of R^n, with Hamiltonian H=H(x,p) being
convex and coercive in p, and establish the uniform convergence of u to an
asymptotic solution as t goes to \infty.

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