# American Institute of Mathematical Sciences

December  2012, 7(4): 857-879. doi: 10.3934/nhm.2012.7.857

## Self-similar solutions in a sector for a quasilinear parabolic equation

 1 Department of Mathematics, Tongji University, Shanghai 200092

Received  January 2012 Revised  October 2012 Published  December 2012

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.
Citation: Bendong Lou. Self-similar solutions in a sector for a quasilinear parabolic equation. Networks & Heterogeneous Media, 2012, 7 (4) : 857-879. doi: 10.3934/nhm.2012.7.857
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