Resolvent positive operators and inhomogeneous boundary conditions. (English) Zbl 1072.35077

Arendt, Wolfgang

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 3, 639-670 (2000).

The author studies the initial-boundary value problem with inhomogeneous Dirichlet boundary condition and shows that the existence of a mild solution of this problem is equivalent to the Dirichlet regularity of the domain. Next the asymptotic behaviour of the solutions is studied.

Reviewer: Leszek Gasiński (Kraków)

MSC:

35K20	Initial-boundary value problems for second-order parabolic equations
47D06	One-parameter semigroups and linear evolution equations

References:

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