Regularity of the free boundary for the porous medium 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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Regularity of the free boundary for the porous medium equation

Authors:	P Daskalopoulos R Hamilton

Institution:	Department of Mathematics, University of California, Irvine, California 92697-3875 ; Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0001

Abstract:	We study the regularity of the free boundary for solutions of the porous medium equation $u_{t}=\Delta u^{m}$ , , on ${\mathcal{R}}^{2} \times 0,T]$ , with initial data $u^{0}=u(x,0)$ nonnegative and compactly supported. We show that, under certain assumptions on the initial data $u^{0}$ , the pressure $f=m\, u^{m-1}$ will be smooth up to the interface $\Gamma = \partial \{ u >0 \}$ , when $0<t\leq T$ , for some . As a consequence, the free-boundary $\Gamma$ is smooth.

Keywords:	Porous medium equation free-boundary $C^{\infty }$-regularity

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