Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution. (English) Zbl 1298.35111
The initial value problems on surfaces of revolution with boundary for a class of quasilinear parabolic equations with variable density is studied. In dependence of the behavior of the density near the boundary, simple conditions for uniqueness or nonuniqueness of solutions are provided.
Reviewer: Jiaqi Mo (Wuhu)
MSC:
| 35K59 | Quasilinear parabolic equations |
| 35K65 | Degenerate parabolic equations |
| 35K67 | Singular parabolic equations |
| 35B51 | Comparison principles in context of PDEs |
Keywords:
porous medium equation; singular quasilinear equations; well-posedness; support of solutions; sub-supersolutionsReferences:
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