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Quasilinear parabolic systems under nonlinear boundary conditions. (English) Zbl 0596.35061
The author proves existence and regularity results for abstract quasilinear parabolic systems of the form $$ (*)\quad \partial u/\partial t+A(t,u)u=f(t,u),\quad B(t,u)u=g(t,u),\quad u(s)=u\sb 0\quad for\quad s<t\le T. $$ An important example for which his results are applicable is the case of elliptic operators $$ A(t,u)u:=-D\sb j(a\sb{jk}(\cdot,t,u)D\sb ku)+a\sb j(\cdot,t,u)D\sb ju. $$ A great variety of problems in applications lead to a system of the form (*). The wide range of applications of the author’s results emphasize the importance of this paper.
Reviewer: R.Sperb

35G10Initial value problems for linear higher-order PDE
35K25Higher order parabolic equations, general
35B30Dependence of solutions of PDE on initial and boundary data, parameters
35R15PDE on infinite-dimensional spaces
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