Lucio Boccardo, Thierry Gallouet, & Juan Luis Vazquez
The purpose of this paper is to prove the existence of solutions for certain types of nonlinear parabolic partial differential equations posed in the whole space, when the data are assumed to be merely locally integrable functions, without any control of their behaviour at infinity. A simple representative example of such an equation is
which admits a unique globally defined weak solution if the initial function is a locally integrable function in , , and the second member is a locally integrable function of and whenever the exponent is larger than 1. The results extend to parabolic equations results obtained by Brezis and by the authors for elliptic equations. They have no equivalent for linear or sub-linear zero-order nonlinearities.
Submitted July 17, 2001. Published September 12, 2001.
Math Subject Classifications: 35K55, 35K65.
Key Words: Nonlinear parabolic equations, global existence, growth conditions.
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|Lucio Boccardo |
Dipartimento di Matematica, Universita di Roma 1
Piazza A. Moro 2, 00185
|Thierry Gallouet |
CMI, Universite de Marseille I
|Juan Luis Vazquez |
Departamento de Matematicas
Universidad Autonoma de Madrid
28049 Madrid, Spain
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