Finite approximate controllability for semilinear heat equations in noncylindrical domains

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.

Finite approximate controllability of Hilfer fractional semilinear differential equations

“…For works on controllability, approximate controllability, and finite approximate controllability of differential and inclusions we refer the reader to [2, 5, 6, 8, 10, 15-19, 21, 22, 31]. It is worth mentioning that Menezes et al [19] investigated the finite approximate controllability for the semilinear heat equation, Mahmudov [18] studied the finite approximate controllability of a semilinear evolution equation in a Hilbert space under the assumption that the linear part of the system is approximately controllability and Mahmudov [16] established, under the assumption that the linear part of the system is approximately controllability, the finite approximate controllability of a nonlocal Sobolev-type evolution equation involving the Caputo fractional derivative.…”

Local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains

“…In 2004, De Menezes et al [11] studied properties of the finite approximated controllability for the following semilinear heat equation:…”