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

The existence of time local C^{\infty} -solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the " L^{\infty} -energy method" developed in our previous paper [16] and a new method based on the theory of evolution equations in the L^{2} -framework whic...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2001, Vol.53 (4), p.745-789
Main Authors: SUGIYAMA, Yoshie, ÔTANI, Mitsuharu
Format: Article
Language:English
Subjects:
35K
C^{\infty}-solution
evolution equation
local existence
nonlinear parabolic
porous medium equation
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Summary:The existence of time local C^{\infty} -solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the " L^{\infty} -energy method" developed in our previous paper [16] and a new method based on the theory of evolution equations in the L^{2} -framework which enables us to handle with perturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/05340745