Free boundary problem for quasilinear parabolic equation with fixed angle of contact to a boundary. (English) Zbl 1005.35094
The author considers a free boundary problem for the equation
\[
u_{t}=(au_{x})_{x}, \qquad s(t)<x<0,\quad t>0,
\]
with corresponding initial, boundary and smoothness conditions. He studies the existence and structure of selfsimilar solutions of this equation. By constructing the subsolution and supersolution he finds the asymptotic convergence of every solution to its selfsimilar solution.
Reviewer: Asaf D.Iskenderov (Baku)
References:
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