Finite-dimensional exact controllability of an abstract semilinear fractional composite relaxation equation
نویسندگان
چکیده
In Hilbert space, the finite-dimensional exact controllability of an abstract semilinear fractional composite relaxation equation is researched. We make assumptions about parameters in and suppose that linear associated with approximately controllable. apply variational method, resolvent theory fixed point trick to demonstrate equation. An application given last paper testify our results.
منابع مشابه
Finite Dimensional Null Controllability for the Semilinear Heat Equation
ABSTRACI’. We study a finite dimensional version of the null controllability problem for semilinear heat equations in bounded domains R of R” with Dirichlet boundary conditions. The control acts on any open an non-empty subset of R. The question under consideration is the following: given an initial state, a control time t = 2’ and a finite dimensional subspace E of L”(n), is there a control su...
متن کاملExact controllability of semilinear evolution equation and applications
where Z, U are Hilbert spaces, A : D(A) ⊂ Z −→ Z is the infinitesimal generator of strongly continuous semigroup {T (t)}t≥0 inZ, B ∈ L(U,Z), the control function u belongs to L(0, τ ;U) and F : [0, τ ]× Z × U −→ Z is a suitable function. First, we give a necessary and sufficient condition for the exact controllability of the linear system z′ = Az + Bu(t); Second, under some conditions on F , we...
متن کاملExact Distributed Controllability for the Semilinear Wave Equation
In this paper we generalize the theorems of exact controllability for the linear wave equation with a distributed control to the semilinear case, showing that, given T large enough, for every initial state in a sufficiently small neighbourhood of the origin in a certain function space, there exists a distributed control, supported on a part of a domain, driving the system to rest. Also, if the ...
متن کاملExact Internal Controllability for the Semilinear Heat Equation
Using Browder-Minty’s surjective theorem from the theory of monotone operators, We consider the exact internal controllability for the semilinear heat equation. We show that the system is exactly controllable in L(Ω) if the nonlinearities are globally Lipschitz continuous. Furthermore, we prove that the controls depend Lipschitz continuously on the terminal states, and discuss the behaviour of ...
متن کاملExact Controllability of Semilinear Systems with Impulses
The purpose of this paper is to investigate the controllability of the impulsive semilinear system x′(t) = A(t)x(t) + f(t, x(t)) + B(t)u(t), t ≥ t0, t 6= tk, x(t+k ) = x(t − k ) + Ik(x(t − k )), k = 1, 2, 3, . . . . By making use of Schaefer’s fixed point theorem we obtain some results under which the system is completely controllable. Two examples are also given to illustrate the importance of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2023
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2308347l