On existence of the weak solution for nonlinear diffusion equation. (English) Zbl 0741.35031

A rather general parabolic equation is considered which includes the cases of fast and slow diffusion. The existence of weak solutions is established by means of the line method. It consists of discretizing the problem with respect to the time variable. The problem then reduces to an elliptic system which can be solved by means of a variational method. A solution to the original equation is obtained by letting the time steps tend to zero.
Reviewer: C.Bandle (Basel)


35K65 Degenerate parabolic equations
35K57 Reaction-diffusion equations
35A15 Variational methods applied to PDEs
65N40 Method of lines for boundary value problems involving PDEs
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