Abstract
We investigate finite approximate controllability for semilinear heat equation in noncylindrical domains. First we study the linearized problem and then by an application of the fixed point result of Leray-Schauder we obtain the finite approximate controllability for the semilinear state equation.
Highlights
AND MAIN RESULTWe consider a semilinear parabolic problem in a domain Q of Rn+1 = Rn × Rt which is not a cylinder, but it is a union of open domains t of Rn, 0 < t < T, images of a reference domain0 by a diffeomorphism τt : 0 → t
In this article we investigate finite approximate controllability for the following semilinear parabolic system u − u + f (u) = h(x, t)χqin Q
There is an extensive literature about finite-approximate controllability for linear and semilinear heat equation in cylindrical domains
Summary
There is an extensive literature about finite-approximate controllability for linear and semilinear heat equation in cylindrical domains. Among these works, it is worth mentioning the articles of Fernandez and Zuazua 1999, Lions 1991 and Zuazua 1997, 1999. In the context of linear heat equation in noncylindrical domains, Limaco et al 2002 proved the finite-approximate controllability. The first step in the fixed point method is to study the finite-approximate controllability for a linearized system. The present paper is organized as follows: Section 2 is devoted to prove the finite-approximate controllability for the linearized system.
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