On a parabolic equation related to the \(p\)-Laplacian. (English) Zbl 1338.35235
Summary: Consider a parabolic equation related to the \(p\)-Laplacian. If the diffusion coefficient of the equation is degenerate on the boundary, no matter we can define the trace of the solution on the boundary or not, by choosing a suitable test function, the stability of the solutions always can be established without a boundary condition.
MSC:
| 35K55 | Nonlinear parabolic equations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 35R35 | Free boundary problems for PDEs |
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