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.
“…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.…”
In this paper, we investigate the finite approximate controllability of fractional semilinear differential equations involving the Hilfer derivative. We show that if the linear part is approximate controllable, then under suitable conditions the semilinear system is finite approximate controllable.
“…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.…”
In this paper, we investigate the finite approximate controllability of fractional semilinear differential equations involving the Hilfer derivative. We show that if the linear part is approximate controllable, then under suitable conditions the semilinear system is finite approximate controllable.
In this paper, we establish a local null controllability result for a nonlinear parabolic PDE with local and nonlocal nonlinearities in a domain whose boundary moves in time by a control force with a multiplicative part acting on a prescribed subdomain. We prove that, if the initial data is sufficiently small and the linearized system at zero satisfies an appropriate condition, the equation can be driven to zero.
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