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Optimal control of quasilinear parabolic equations*

Published online by Cambridge University Press:  14 November 2011

Eduardo Casas ,
Luis A. Fernández  and
Jiongmin Yong
Eduardo Casas
Affiliation:
Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. de Caminos, Universidad de Cantabria, 39071 Santander, Spain
Luis A. Fernández
Affiliation:
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain
Jiongmin Yong
Affiliation:
Department of Mathematics, Fudan University, Shanghai 200433, China
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Extract

This paper deals with optimal control problems governed by quasilinear parabolic equations in divergence form, whose cost functional is of Lagrangian type. Our aim is to prove the existence of solutions and derive some optimality conditions. To attain this second objective, we accomplish the sensitivity analysis of the state equation with respect to the control, proving that, under some assumptions, this relation is Gâteaux differentiable. Finally, a regularising procedure along with Ekeland's variational principle allow us to treat some other problems for which this differentiability property cannot be stated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 3 , 1995 , pp. 545 - 565
Copyright
Copyright © Royal Society of Edinburgh 1995

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