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Flux limited generalized porous media diffusion equations. (English) Zbl 1282.35205

Summary: We study a class of generalized porous media type flux limited diffusion equations and we prove the existence and uniqueness of entropy solutions. We compute the Rankine-Hugoniot condition on the jump set for solutions which are of locally bounded variation in space and time. We give also a geometric characterization of the entropy conditions on the jump set for a restricted class of this type of equations.

MSC:

35K65 Degenerate parabolic equations
35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35D30 Weak solutions to PDEs
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