Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation

Authors:	Email author" target="_blank">Piotr?Biler Email author Grzegorz?Karch Mohammed?Guedda

Institution:	(1) Instytut Matematyczny, Uniwersytet Wrocawski, pl. Grundwaldzki 2/4, 50-384 Wrocaw, Poland;(2) L.A.M.F.A./CNRS FRE 2270, Faculté de Mathématiques et dInformatique, Université de Picardie-Jules Verne, 33, rue Saint-Leu, 80039 Amiens, France

Abstract:	The purpose of the paper is to study properties of solutions of the Cauchy problem for the equation $u_t-\Delta u + \|\nabla u\|^q=0$ under the assumption . General selfsimilar solutions are constructed. Moreover, for initial data with some decay at infinity, we determine the leading term of the asymptotics of solutions in $L^p(\mathbb{R}^n)$ which is described by either solutions of the linear heat equation or by particular selfsimilar solutions of the original equation.

Keywords:	35B40 35K55 35Q99
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