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Title: On the doubly singular equation g(u)t= Dpu
Authors: Henriques, Eurica 
Urbano, José Miguel 
Keywords: Doubly singular PDE; Regularity theory; Intrinsic scaling; Phase transition
Issue Date: 2004
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 04-07 (2004)
Abstract: We prove that local weak solutions of a nonlinear parabolic equation with a doubly singular character are locally continuous. One singularity occurs in the time derivative and is due to the presence of a maximal monotone graph; the other comes up in the principal part of the PDE, where the p-Laplace operator is considered. The paper extends to the singular case 1 < p < 2, the results obtained previously by the second author for the degenerate case p > 2; it completes a regularity theory for a type of PDEs that model phase transitions for a material obeying a nonlinear law of di usion.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Nacionais

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