Well-posedness for a family of degenerate parabolic mixed equations

2020/05/11 by Acevedo, Ramiro, Gómez, Christian, Rodríguez, Bibiana López
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2005.05429

Abstract

The aim of this work is to show an abstract framework to analyze a family of linear degenerate parabolic mixed equations. We combine the theory for the degenerate parabolic equations with the classical Babuska-Brezzi theory for linear mixed stationary equations to deduce sufficient conditions to prove the well-posedness of the problem. Finally, we illustrate the application of the abstract framework through examples that come from physical science applications including fluid dynamics models and electromagnetic problems.

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