Remarks on a Nonlinear Parabolic 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

Remarks on a Nonlinear Parabolic Equation

Authors:	Matania Ben-Artzi Jonathan Goodman Arnon Levy

Affiliation:	Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel ; Courant Institute of Mathematical Sciences, New York, New York 10012 ; Courant Institute of Mathematical Sciences, New York, New York 10012

Abstract:	The equation $u_{t} =Delta u +mu \|nabla u \|$ , , is studied in $mathbb{R}^{n}$ and in the periodic case. It is shown that the equation is well-posed in $L^{1}$ and possesses regularizing properties. For nonnegative initial data and the solution decays in $L^{1}(mathbb{R}^{n})$ as . In the periodic case it tends uniformly to a limit. A consistent difference scheme is presented and proved to be stable and convergent.

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