SINGULARLY NON-AUTONOMOUS SEMILINEAR PARABOLIC PROBLEMS WITH CRITICAL EXPONENTS

Carvalho, Alexandre N.; Nascimento, Marcelo J. D.

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

SINGULARLY NON-AUTONOMOUS SEMILINEAR PARABOLIC PROBLEMS WITH CRITICAL EXPONENTS

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Author(s):	Carvalho, Alexandre N. ^[1] ; Nascimento, Marcelo J. D. ^[2] Total Authors: 2
Affiliation:	^[1] Univ Sao Paulo, Inst Ciencias Matemat Comp, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil ^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S; v. 2, n. 3, p. 449-471, SEP 2009.
Web of Science Citations:	7
Abstract
In this work we consider initial value problems of the form [dx/dt + A(t)x = f(t, x) x(tau) = x(0), in a Banach space X where A(t) : D subset of X -> X is a linear, closed and unbounded operator which is sectorial for each t. We show local well posedness for the case when the nonlinearity f grows critically. Applications to semilinear parabolic equations and strongly damped wave equations are considered. (AU)

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