Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms

We consider a general class of parabolic equations of the type with Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (W−1, p′). Using the framework of renormalized solutions we prove uniqueness results under appropriate growth conditions and Lipschitz-type conditions on...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2013-12, Vol.143 (6), p.1185-1208
Main Authors: Nardo, Rosaria Di, Feo, Filomena, Guibé, Olivier
Format: Article
Language:English
Subjects:
Boundary conditions
Dirichlet problem
Mathematical analysis
Mathematics
Nonlinearity
Uniqueness
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Summary:We consider a general class of parabolic equations of the type with Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (W−1, p′). Using the framework of renormalized solutions we prove uniqueness results under appropriate growth conditions and Lipschitz-type conditions on a(u, ∇u), K(u) and H(∇u).
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210511001831