Existence and Uniqueness of a Weak Solution to the Initial Mixed Boundary-Value Problem for Quasilinear Elliptic-Parabolic Equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Existence and Uniqueness of a Weak Solution to the Initial Mixed Boundary-Value Problem for Quasilinear Elliptic-Parabolic Equations

Authors:

A V Ivanov J F Rodrigues

Abstract:

We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation

$\begin{gathered} \partial _t b(u) - {\text{div\{ }}\left| {\delta {\text{(}}u{\text{)}}} \right|^{m - 2} \delta {\text{(}}u{\text{)\} = }}f{\text{(}}x,t{\text{),}} \hfill \\ \delta {\text{(}}u{\text{): = }}\nabla u + k(b(u))\vec e,{\text{ }}\left| {\vec e} \right| = 1,m >1, \hfill \\ \end{gathered}$

with a monotone nondecreasing continuous function b. Such equations arise in the theory of non-Newtonian filtration as well as in the mathematical glaciology. Bibliography: 16 titles.

Keywords:

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