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 B
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.File in questo prodotto:
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