Selfsimilar Solutions in a Sector for a Quasilinear Parabolic Equation

Details Selfsimilar Solutions in a Sector for a Quasilinear Parabolic Equation Selfsimilar Solutions in a Sector for a Quasilinear Parabolic Equation

2010-08-21

arxiv.org/abs/1008.3626v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

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

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