• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.361-376
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• 2000

Our purpose is to seek that the reachable set of the semilinear system $\frac{d}{dt}x(t){\;}={\;}Ax(t){\;}+{\;}f(t,x(t)){\;}+{\;}Bu(t)$ is equivalent to that of its corresponding to linear system (the case where f=0).Under the assumption that the system of generalized eigenspaces of A is complete, we will show that the reachable set corresponding to the linear system is independent of t in case A generates $C_0-semigroup$. An illustrative example for retarded system with time delay is given in the last section.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.189-207
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• 2021

In this paper, we consider the approximate controllability for a class of semilinear integro-differential functional control equations in which nonlinear terms of given equations satisfy quasi-homogeneous properties. The main method used is to make use of the surjective theorems that is similar to Fredholm alternative in the nonlinear case under restrictive assumptions. The sufficient conditions for the approximate controllability is obtain which is different from previous results on the system operator, controller and nonlinear terms. Finally, a simple example to which our main result can be applied is given.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1284-1288
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• 1990

In this paper, we are going to study the stabilization of the semilinear heat equation with inhomogenous boundary conditions, whose solutions are not (in general) stable. Here, we use the discrete-time feedback inputs through the boundary of geometric domain to the semilinear system under some additional conditions and assumptions. It is shown that under these conditions, the stabilization can be realized by applying pole assignment argument to the principal linear part of the system and that the solutions exist globally in discrete-time t without any finite escape time.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.355-368
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• 2021

In this paper, we investigate necessary and sufficient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

• East Asian mathematical journal
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• v.35 no.5
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• pp.535-545
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• 2019

This paper is concerned with the optimal control problem associated to strong solution of Belousov-Zhabotinskii reaction model in 2D domain. That is, we otain the global existence of strong solution and show the existence of optimal control.

• East Asian mathematical journal
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• v.6 no.1
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• pp.77-93
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• 1990

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.603-611
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• 1996

Let consider the following problem: find an element u(t) in a Banach space U from the equation $$ x'(t) = Ax(t) + f(t,x(t)) + \Phi_0 u(t), 0 \leq t \leq T $$ with initial and terminal conditions $$ x(0) = 0, x(T) = \phi $$ in a Banach space X where $\phi \in D(A)$. This problem is a kind of control engineering inverse problem and contains nonlinear term, so that it is difficult and interesting. Thee proof main result in this paper is based on the Fredholm property of [1] in section 3. Similar considerations of linear system have been dealt with in many references. Among these literatures, Suzuki[5] introduced this problem for heat equation with unknown spatially-varing conductivity. Nakagiri and Yamamoto[2] considered the identifiability problem, which A is a unknown operator to be identified, where the system is described by a linear retarded functional differential equation. We can also apply to determining the magnitude of the control set for approximate controllability if X is a reflexive space, i.e., we can consider whether a dense subset of X is covered by reachable set in section 4.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.299-315
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• 2022

This manuscript deals with the exact (complete) controllability of semilinear stochastic differential equations with infinite delay and Poisson jumps utilizing some basic and readily verified conditions. The results are obtained by using fixed-point approach and by using advance phase space definition for infinite delay part. We have used the axiomatic definition of the phase space in terms of stochastic process to consider the time delay of the system. An infinite delay along with the Poisson jump is the new investigation for the given stochastic system. An example is given to illustrate the effectiveness of the results.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.131-145
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• 1991

The purpose of this paper is to prove the approximate controllability results, which were shown in [4] for the abstract semilinear control system, here, for the delay volterra system in the case of trajectories.