Asymptotic solutions for large time of Hamilton–Jacobi equations in Euclidean n space
Hitoshi Ishii
Department of Mathematics, Faculty of Education and Integrated Arts and Sciences, Waseda University, Tokyo, 169-8050 Japan
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Abstract
We study the large time behavior of solutions of the Cauchy problem for the Hamilton–Jacobi equation in , where is continuous on and convex in . We establish a general convergence result for viscosity solutions of the Cauchy problem as .
Résumé
Nous étudions le comportement en temps grand des solutions du problème de Cauchy pour l'équation de Hamilton–Jacobi dans , où est continu dans et convexe en . Nous établissons un résultat de convergence général pour les solutions de viscosité du problème de Cauchy quand .
Cite this article
Hitoshi Ishii, Asymptotic solutions for large time of Hamilton–Jacobi equations in Euclidean n space. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 2, pp. 231–266
DOI 10.1016/J.ANIHPC.2006.09.002