Strongly damped wave problems: Bootstrapping and regularity of solutions |
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Authors: | AN Carvalho JW Cholewa Tomasz Dlotko |
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Institution: | a Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil b Institute of Mathematics, Silesian University, 40-007 Katowice, Poland |
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Abstract: | The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. |
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Keywords: | primary 35L05 secondary 35B33 35B65 |
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