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Local existence and uniqueness of solutions of degenerate parabolic equations. (English) Zbl 0738.35033
Author’s summary: We consider a class of degenerate parabolic equations on a bounded domain with mixed boundary conditions. These problems arise, for example, in the study of flow through porous media. Under appropriate hypotheses, we establish the existence of a nonnegative solution which is obtainable as a monotone limit of solutions of quasilinear parabolic equations. This construction is used to establish uniqueness, comparison, and L 1 continuous dependence theorems, as well as some results on blow up of solutions in finite time.

35K65Parabolic equations of degenerate type
35Q35PDEs in connection with fluid mechanics
35A07Local existence and uniqueness theorems (PDE) (MSC2000)
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
76S05Flows in porous media; filtration; seepage
35B30Dependence of solutions of PDE on initial and boundary data, parameters
35B65Smoothness and regularity of solutions of PDE