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Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data

Local estimates and global existence for strongly nonlinear parabolic equations with locally... We obtain existence results for some strongly nonlinear Cauchy problems posed in $$ {\mathbb{R}^{N} } $$ and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudomonotone operator of Leray-Lions type acting on $$ L^{P} {\left( {0,\,T;\,W^{{1,p}}_{{{\text{loc}}}} {\left( {\mathbb{R}^{N} } \right)}} \right)} $$ , they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-005-0234-7
Publisher site
See Article on Publisher Site

Abstract

We obtain existence results for some strongly nonlinear Cauchy problems posed in $$ {\mathbb{R}^{N} } $$ and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudomonotone operator of Leray-Lions type acting on $$ L^{P} {\left( {0,\,T;\,W^{{1,p}}_{{{\text{loc}}}} {\left( {\mathbb{R}^{N} } \right)}} \right)} $$ , they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence results.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Feb 1, 2006

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