We obtain existence results for some strongly nonlinear Cauchy problems posed in R^N and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudo-monotone operator of Leray-Lions type acting on L^p (0, T ; W^{1,p}(R^N )), 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.

Local estimates and global existence for nonlinear parabolic equations with absorbing lower order terms

PELLACCI, Benedetta
2006

Abstract

We obtain existence results for some strongly nonlinear Cauchy problems posed in R^N and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudo-monotone operator of Leray-Lions type acting on L^p (0, T ; W^{1,p}(R^N )), 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/20258
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