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Linear parabolic problems involving measures


Amann, H (2001). Linear parabolic problems involving measures. Real Academia de Ciencias Exactas, Fisicas y Naturales. Revista. Serie A, Matematicas, 95(1):85-119.

Abstract

We develop a general solvability theory for linear evolution equations of the form u˙+Au=μ on R+, where −A is the infinitesimal generator of a strongly continuous analytic semigroup, and μ is a bounded Banach-space-valued Radon measure. It is based on the theory of interpolation-extrapolation spaces and the Riesz representation theorem for such measures.
"The abstract results are illustrated by applications to second-order parabolic initial value problems. In particular, the case where Radon measures occur on the Dirichlet boundary can be handled, which is important in control theory and has not been treated so far.
"We also give sharp estimates under various regularity assumptions. They form the basis for the study of semilinear parabolic evolution equations with measures, which is to be studied in a forthcoming joint paper of the author and P. Quittner.

We develop a general solvability theory for linear evolution equations of the form u˙+Au=μ on R+, where −A is the infinitesimal generator of a strongly continuous analytic semigroup, and μ is a bounded Banach-space-valued Radon measure. It is based on the theory of interpolation-extrapolation spaces and the Riesz representation theorem for such measures.
"The abstract results are illustrated by applications to second-order parabolic initial value problems. In particular, the case where Radon measures occur on the Dirichlet boundary can be handled, which is important in control theory and has not been treated so far.
"We also give sharp estimates under various regularity assumptions. They form the basis for the study of semilinear parabolic evolution equations with measures, which is to be studied in a forthcoming joint paper of the author and P. Quittner.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Banach space valued Radon measure; analytic semigroup; existence, regularity and continuity theorems
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Real Academia de Ciencias Exactas Fisicas y Naturales
ISSN:1578-7303
Additional Information:© Real Academia de Ciencias 2001
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1018.35049
http://www.rac.es//4/4_3_2_1.php?id=9
Permanent URL: https://doi.org/10.5167/uzh-21986

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