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Existence and regularity for semilinear parabolic evolution equations. (English) Zbl 0625.35045
We study semilinear parabolic systems with linear time dependent boundary conditions. There are given existence and regularity theorems and they are obtained by means of semigroup methods. Due to the time dependent boundary conditions the usual approach via fractional power spaces is not suitable. For this reason we develop a theory in interpolation spaces which permits also a treatment of parabolic systems in \(W^ s_ p\) for \(s>0\). By this method we can easily prove that the constructed mild solutions of the associated abstract problem are in fact classical solutions of the parabolic system.

MSC:
35K55 Nonlinear parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
47D03 Groups and semigroups of linear operators
35B65 Smoothness and regularity of solutions to PDEs
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