Far Eastern Mathematical Journal

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Solvability of a quasi-linear parabolic equation in the domain with a piecewise monotone boundary


Podgaev A. G., Lisenkov K. V.

2013, issue 2, Ń. 250-272


Abstract
We investigate the existence of regular solutions for the quasilinear parabolic equation in non-cylindrical domain with a boundary of class$W_2^1$. The equation can degenerate but point degenerates depend from solution. Approximate solutions are constructed using the projection method of the family of projectors depending on the time parameter. We prove that a limit of these solutions will be the solution of the problem. To justify the existence of the limit solution are used compactness methods functions from scale of Banach spaces.

Keywords:
existence, a quasi-linear parabolic equation, non-cylindrical domains, the projection method, the compactness, the scale of Banach spaces

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