On existence of the weak solution for nonlinear diffusion equation (Q1176966)
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scientific article; zbMATH DE number 12776
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On existence of the weak solution for nonlinear diffusion equation |
scientific article; zbMATH DE number 12776 |
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On existence of the weak solution for nonlinear diffusion equation (English)
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25 June 1992
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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.
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bounded weak solutions
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nonhomogeneous mixed boundary conditions
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initial-boundary value problem
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nonlinear diffusion
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