Stability of degenerate parabolic Cauchy problems

Teemu Lukkari; Mikko Parviainen

doi:10.3934/cpaa.2015.14.201

Article Contents

2015, Volume 14, Issue 1: 201-216. Doi: 10.3934/cpaa.2015.14.201

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Stability of degenerate parabolic Cauchy problems

Teemu Lukkari^1, and
Mikko Parviainen^1,

1.
Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyväskylä

Received: December 31, 2013

Revised: January 31, 2014

Published: December 2014

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Abstract

We prove that solutions to Cauchy problems related to the $p$-parabolic equations are stable with respect to the nonlinearity exponent $p$. More specifically, solutions with a fixed initial trace converge in an $L^q$-space to a solution of the limit problem as $p>2$ varies.

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Mathematics Subject Classification: Primary: 35K55; Secondary: 35K15, 35K65.

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