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- Title
The trace triple for nonnegative solutions of the porous medium equation.
- Authors
Chou, Kai-Seng; Kwong, Ying-Chuen
- Abstract
It is shown that, for every non-negative weak solution u of the generalized porous medium Eq. (1) Ψ(u) takes a Radon measure as its lateral trace. When Ψ(u) is integrable, u has an initial trace consisting of a bottom measure and a corner measure. The initial trace (bottom and corner measures) and the lateral trace form the trace triple for the solution. The initial-Dirichlet problem of prescribing trace triple is solved for the porous medium equation in the slow diffusion case.
- Subjects
NONNEGATIVE matrices; RADON measures; DIRICHLET problem; POROUS materials; PROBLEM solving
- Publication
Calculus of Variations & Partial Differential Equations, 2019, Vol 58, Issue 1, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-018-1475-y