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Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces. (English) Zbl 1389.37044

The author studies general inhomogeneous initial-boundary value problems for parabolic equations with a single spatial variable. The equations are considered in anisotropic Hörmander spaces of functional regularity indices. Theorems of isomorphism are proved. This extends earlier results on the Cauchy problem for general parabolic equations and parabolic problems of the second order with inhomogeneous initial conditions; see [the first author et al., Commun. Pure Appl. Anal. 16, No. 1, 69–97 (2017; Zbl 1361.35072); Open Math. 15, 57–76 (2017; Zbl 1372.35132)].

MSC:

37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
58D25 Equations in function spaces; evolution equations
35K30 Initial value problems for higher-order parabolic equations
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