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Asymptotic analysis for the eikonal equation with the dynamical boundary conditions
Author(s) -
AlAidarous Eman S.,
Alzahrani Ebraheem O.,
Ishii Hitoshi,
Younas Arshad M. M.
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300224
Subject(s) - eikonal equation , mathematics , hamilton–jacobi equation , limit (mathematics) , mathematical analysis , boundary value problem , asymptotic analysis , convergence (economics) , boundary (topology) , zero (linguistics) , dynamical systems theory , physics , linguistics , philosophy , economics , economic growth , quantum mechanics
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.