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Analysis and optimal control of some quasilinear parabolic equations

  • Corresponding author: Eduardo Casas

    Corresponding author: Eduardo Casas 

Dedicated to Prof. Jiongmin Yong on the occasion of his 60th birthday

The first author was partially supported by the Spanish Ministerio de Economía, Industria y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P

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  • In this paper, we consider optimal control problems associated with a class of quasilinear parabolic equations, where the coefficients of the elliptic part of the operator depend on the state function. We prove existence, uniqueness and regularity for the solution of the state equation. Then, we analyze the control problem. The goal is to get first and second order optimality conditions. To this aim we prove the necessary differentiability properties of the relation control-to-state and of the cost functional.

    Mathematics Subject Classification: Primary: 35K59, 49K20; Secondary: 49J20.

    Citation:

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