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Zbl 1072.35077
Arendt, Wolfgang
Resolvent positive operators and inhomogeneous boundary conditions. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 3, 639-670 (2000). ISSN 0391-173X

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.
[Leszek Gasiński (Kraków)]
MSC 2000:
*35K20 Second order parabolic equations, boundary value problems
47D06 One-parameter semigroups and linear evolution equations

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