A method of energy estimates in L∞ and its application to porous medium equations

Mitsuharu Otani; Yoshie Sugiyama

A method of energy estimates in L^∞ and its application to porous medium equations

Mitsuharu Otani^*, Yoshie Sugiyama

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The existence of time local C^∞-solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the "L^∞-energy method" developed in our previous paper [16] and a new method based on the theory of evolution equations in the L²-framework which enables us to handle with porturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.

Original language	English
Pages (from-to)	1-789
Number of pages	789
Journal	Journal of the Mathematical Society of Japan
Volume	53
Issue number	4
Publication status	Published - 2001 Oct

Keywords

C-solution
Evolution equation
Local existence
Nonlinear parabolic
Porous medium equation

ASJC Scopus subject areas

Mathematics(all)

Cite this

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AB - The existence of time local C∞-solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the "L∞-energy method" developed in our previous paper [16] and a new method based on the theory of evolution equations in the L2-framework which enables us to handle with porturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.

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KW - Evolution equation

KW - Local existence

KW - Nonlinear parabolic

KW - Porous medium equation

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ER -

A method of energy estimates in L^∞ and its application to porous medium equations

Abstract

Keywords

ASJC Scopus subject areas

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