The Large-time Behavior of Solutions of Hamilton-Jacobi Equations on the Real Line

• DOI: 10.4310/maa.2008.v15.n2.a8
• Publication Date: 2013-08-31T00:12:38Z
• Authors: Naoyuki Ichihara; Hitoshi Ishii
• Keywords: asymptotic solutions; 49L25; 35B40; 70H20; Large-time behavior; 0101 mathematics; Hamilton-Jacobi equations; 01 natural sciences

We investigate the large-time behavior of solutions of the Cauchy problem for Hamilton-Jacobi equations on the real line R. We establish a result on convergence of the solutions to asymptotic solutions as time t goes to infinity.