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Zbl 0738.35033
Anderson, Jeffrey R.
Local existence and uniqueness of solutions of degenerate parabolic equations. (English)
[J] Commun. Partial Differ. Equations 16, No.1, 105-143 (1991). ISSN 0360-5302; ISSN 1532-4133/e

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 $L\sp 1$ continuous dependence theorems, as well as some results on blow up of solutions in finite time.
[A.D.Osborne (Keele)]

MSC 2000:: *35K65 Parabolic equations of degenerate type
35Q35 Other equations arising in fluid mechanics
35A07 Local existence and uniqueness theorems (PDE)
35B05 General behavior of solutions of PDE
76S05 Flows in porous media
35B30 Dependence of solutions of PDE on initial and boundary data
35B65 Smoothness of solutions of PDE

Keywords: mixed boundary conditions; uniqueness; comparison; continuous dependence theorems; blow up of solutions in finite time

Cited in: Zbl 0990.35081 Zbl 0884.35074

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