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

Published online by Cambridge University Press:  03 December 2013

Rosaria Di Nardo ,
Filomena Feo  and
Olivier Guibé
Rosaria Di Nardo
Affiliation:
Dipartimento di Matematica, Seconda Università degli Studi di Napoli, viale Lincoln, 5-81100 Caserta, Italy ([email protected])
Filomena Feo
Affiliation:
Dipartimento di Ingegneria, Università degli Studi di Napoli Parthenope, Isola C4, Centro Direzionale, 80100 Naples, Italy ([email protected])
Olivier Guibé
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, CNRS, Avenue de l'Université, BP 12, Technopôle du Madrillet, 76801 Saint Etienne du Rouvray, France ([email protected])
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Abstract

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).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 6 , December 2013 , pp. 1185 - 1208
Copyright
Copyright © Royal Society of Edinburgh 2013 

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