Well-posedness of a family of degenerate parabolic mixed equations. (English) Zbl 1460.78026
Summary: In this study, we present an abstract framework for analyzing a family of linear degenerate parabolic mixed equations. We combine the theory of degenerate parabolic equations with the classical Babuška-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 based on examples from physical science applications, including fluid dynamics models and electromagnetic problems.
MSC:
| 78M30 | Variational methods applied to problems in optics and electromagnetic theory |
| 76M30 | Variational methods applied to problems in fluid mechanics |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 35K65 | Degenerate parabolic equations |
| 35M10 | PDEs of mixed type |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 65J08 | Numerical solutions to abstract evolution equations |
Keywords:
well-posedness; time-dependent problems; parabolic degenerate equations; mixed equations; Stokes problem; eddy current modelReferences:
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