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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 \[ (*)\quad \partial u/\partial t+A(t,u)u=f(t,u),\quad B(t,u)u=g(t,u),\quad u(s)=u_ 0\quad for\quad s<t\leq T. \] An important example for which his results are applicable is the case of elliptic operators \[ A(t,u)u:=-D_ j(a_{jk}(\cdot,t,u)D_ ku)+a_ j(\cdot,t,u)D_ ju. \] 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

MSC:
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
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