On parabolic final value problems and well-posedness

被引:4
|
作者
Christensen, Ann-Eva [1 ,2 ]
Johnsen, Jon [1 ]
机构
[1] Aalborg Univ, Dept Math, Skjernvej 4A, DK-9220 Aalborg, Denmark
[2] Aalborg Univ Hosp, Unit Epidemiol & Biostat, Hobrovej 18-22, DK-9000 Aalborg, Denmark
关键词
OPERATORS;
D O I
10.1016/j.crma.2018.01.019
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that a large class of parabolic final value problems is well posed. This results via explicit Hilbert spaces that characterise the data yielding existence, uniqueness and stability of solutions. This data space is the graph normed domain of an unbounded operator, which represents a new compatibility condition pertinent for final value problems. The framework is that of evolution equations for Lax-Milgram operators in vector distribution spaces. The final value heat equation on a smooth open set is also covered, and for non-zero Dirichlet data, a non-trivial extension of the compatibility condition is obtained by addition of an improper Bochner integral. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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页码:307 / 311
页数:5
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