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Local well posedness for strongly damped wave equations with critical nonlinearities

Published online by Cambridge University Press:  17 April 2009

Alexandre N. Carvalho  and
Jan W. Cholewa
Alexandre N. Carvalho
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo - Campus de São Carlos, Caixa Postal 668, 13.560–970 São Carlos SP, Brazil e-mail: andcarva@icmc.sc.usp.br
Jan W. Cholewa
Affiliation:
Institute of Mathematics, Silesian University, 40–007 Katowice, Poland e-mail: jcholewa@ux2.math.us.edu.pl
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In this article the strongly damped wave equation is considered and a local well posedness result is obtained in the product space . The space of initial conditions is chosen according to the energy functional, whereas the approach used in this article is based on the theory of analytic semigroups as well as interpolation and extrapolation spaces. This functional analytic framework allows local existence results to be proved in the case of critically growing nonlinearities, which improves the existing results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 443 - 463
Copyright
Copyright © Australian Mathematical Society 2002

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