• Journal of the Korean Mathematical Society
• /
• v.40 no.5
• /
• pp.769-788
• /
• 2003

In this paper, we study the optimal control for the damped semilinear hyperbolic systems with unknown parameters (C(t)y')'＋ $A_2$(t, q)y'＋ $A_1$(t, q)y = f(t, q, y, u). We will prove the existence of weak solution of this system and is to find the optimal control pair (q, u) $\in$ $Q_{t}$ ${\times}$ $U_{ad}$ such that in $f_{u}$$\in$ $Q_{t}$/ J(q, u) = J(q, u).$_{t}$/ J(q, u) = J(q, u).

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.1
• /
• pp.25-32
• /
• 2011

In this paper, we study the existence and uniqueness of solutions for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions and forcing term with memory in n-dimensional fuzzy vector space ($E^n_N$, $d_{\varepsilon}$) by using Banach fixed point theorem. That is an extension of the result of Kwun et al. [9] to impulsive system.

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

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

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

• Honam Mathematical Journal
• /
• v.19 no.1
• /
• pp.71-80
• /
• 1997

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

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.1-28
• /
• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

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

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