Doubly nonlinear evolution equations associated with elliptic-parabolic free boundary problems

Noriaki Yamazaki

doi:10.3934/proc.2005.2005.920

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2005, Volume 2005: 920-929. Doi: 10.3934/proc.2005.2005.920 open access

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Doubly nonlinear evolution equations associated with elliptic-parabolic free boundary problems

Noriaki Yamazaki^1,

1.
Department of Mathematical Science, Common Subject Division, Muroran Institute of Technology, 27-1 Mizumoto-chō, Muroran

Received: August 31, 2004

Revised: February 28, 2005

Published: August 2005

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Abstract

We study an abstract doubly nonlinear evolution equation associated with elliptic-parabolic free boundary problems. In this paper we show the existence and uniqueness of solution for the doubly nonlinear evolution equation. Moreover we apply our abstract results to an elliptic-parabolic free boundary problem.

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Mathematics Subject Classification: Primary: 35K90, 35R70; Secondary: 35R35.

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