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Optimal control problems governed by semilinear parabolic equations with low regularity data


Amann, H; Quittner, P (2006). Optimal control problems governed by semilinear parabolic equations with low regularity data. Advances in Differential Equations, 11(1):1-33.

Abstract

We study optimal controls problems with final observation. The
governing parabolic equations or systems involve superlinear nonlinearities and
their solutions may blow up in finite time. Our proof of the existence, regularity
and optimality conditions for an optimal pair is based on uniform a priori
estimates for the approximating solutions. Our conditions on the growth of the
nonlinearity are essentially optimal. In particular, we also solve a longstanding
open problem of J.L. Lions concerning singular systems.

Abstract

We study optimal controls problems with final observation. The
governing parabolic equations or systems involve superlinear nonlinearities and
their solutions may blow up in finite time. Our proof of the existence, regularity
and optimality conditions for an optimal pair is based on uniform a priori
estimates for the approximating solutions. Our conditions on the growth of the
nonlinearity are essentially optimal. In particular, we also solve a longstanding
open problem of J.L. Lions concerning singular systems.

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Citations

1 citation in Web of Science®
2 citations in Scopus®
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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
Language:English
Date:2006
Deposited On:04 Jan 2010 14:15
Last Modified:06 Dec 2017 20:44
Publisher:Khayyam
ISSN:1079-9389
Free access at:Related URL. An embargo period may apply.
Official URL:http://www.aftabi.com/ADE/ADE-11-figs/p1.gif
Related URLs:http://user.math.uzh.ch/amann/files/aq4-2.pdf

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