|
|||||
|
|
Asymptotic analysis for the eikonal equation with the dynamical boundary conditions |
|
| Authors: | Eman S Al‐Aidarous Ebraheem O Alzahrani Hitoshi Ishii Arshad M M Younas |
| Institution: | 1. Department of Mathematics, Faculty of Science, King Abdulaziz University, , P. O. Box 80203 Jeddah, 21589 Saudi Arabia;2. Faculty of Education and Integrated Arts and Sciences, Waseda University, , Shinjuku, Tokyo 169‐8050, Japan |
| Abstract: | We study the dynamical boundary value problem for Hamilton‐Jacobi equations of the eikonal type with a small parameter. We establish two results concerning the asymptotic behavior of solutions of the Hamilton‐Jacobi equations: one concerns with the convergence of solutions as the parameter goes to zero and the other with the large‐time asymptotics of solutions of the limit equation. |
| Keywords: | Asymptotic behavior eikonal equations dynamical boundary conditions Hamilton‐Jacobi equations MSC (2010) 35F21 35B40 35D40 35F31 49L25 |