Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions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

Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions

Authors:	Masataka Nishikawa Kenji Nishihara

Affiliation:	Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan ; School of Political Science and Economics, Waseda University Tokyo, 169-50, Japan

Abstract:	This paper is concerned with the asymptotic behavior of the solution toward the planar rarefaction wave $r(frac{x}{t})$ connecting $u_{+}$ and $u_{-}$ for the scalar viscous conservation law in two space dimensions. We assume that the initial data $u_{0}(x,y)$ tends to constant states $u_{pm }$ as , respectively. Then, the convergence rate to $r(frac{x}{t})$ of the solution is investigated without the smallness conditions of $\|u_{+}-u_{-}\|$ and the initial disturbance. The proof is given by elementary $L^{2}$ -energy method.

Keywords:	Nonlinear stable viscous conservation law planar rarefaction wave $L^2$-energy method.

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