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arXiv · 1008.3626

Selfsimilar solutions in a sector for a quasilinear parabolic equation

Bendong Lou
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Abstract

We study a two-point free boundary problem in a sector for a quasilinear parabolic equation. The boundary conditions are assumed to be spatially and temporally "self-similar" in a special way. We prove the existence, uniqueness and asymptotic stability of an expanding solution which is self-similar at discrete times. We also study the existence and uniqueness of a shrinking solution which is self-similar at discrete times.

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Bendong Lou. 2010-08-21. Selfsimilar solutions in a sector for a quasilinear parabolic equation. https://doi.org/10.3934/nhm.2012.7.857

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