Boundary value problems for parabolic systems
type: Item
instance of: scholarly article
title: Boundary value problems for parabolic systems
zbMATH Open document ID: 0582.35053
author: Luisa Fattorusso
published in: Ricerche di Matematica
publication date: 1984-01-01T00:00:00Z
review text: Existence and uniqueness theorems are proved for weak solutions of a specified class of second order parabolic boundary value problems. The case of bounded domains \(Q=\Omega \times (0,T)\subset R^{n+1}\) is considered first. Subject to various technical hypotheses, an existence and uniqueness theorem is proved, and estimates for the solution are given in the space \(L^ 2(0,T;V)\cap L^{2,\infty}(Q),\) where V contains \(H^ 1_ 0(\Omega)\). Unlike previous results of this type, the estimates obtained are independent of T. Similar results, depending on the measure of \(\Omega\), and on T, were obtained by M. Marino. In the final section these results are generalized to unbounded domains. The results are related to those of O. Arena, though with different hypotheses.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 3931557
zbMATH Keywords: Existence
zbMATH Keywords: uniqueness
zbMATH Keywords: weak solutions
zbMATH Keywords: estimates
zbMATH Keywords: unbounded domains
reviewed by: Allan L. Edelson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3931557