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On the solvability of nonlocal pluriparabolic problems. (English) Zbl 0968.35067

Summary: The aim of this paper is to prove existence, uniqueness, and continuous dependence upon the data of solutions to mixed problems for pluriparabolic equations with nonlocal boundary conditions. The proofs are based on a priori estimates established in non-classical function spaces and on the density of the range of the operator generated by the studied problems.

MSC:

35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35B45 A priori estimates in context of PDEs
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
35D05 Existence of generalized solutions of PDE (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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