We study the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation u_t+\alpha x Du +H(Du)=f(x) in R^n x [0;+\infty)$, where \alpha is a positive constant and H is a convex function on R^n, and establish a convergence result for the viscosity solution u(x,t) as t -> +infty.
Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space / Fujita, Y; Ishii, H; Loreti, Paola. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 55:(2006), pp. 1671-1700. [10.1512/iumj.2006.55.2813]
Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space.
LORETI, Paola
2006
Abstract
We study the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation u_t+\alpha x Du +H(Du)=f(x) in R^n x [0;+\infty)$, where \alpha is a positive constant and H is a convex function on R^n, and establish a convergence result for the viscosity solution u(x,t) as t -> +infty.File allegati a questo prodotto
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