Jin-Mun Jeong

Approximate Controllability for Semilinear Retarded Functional Differential Equations

This paper deals with the approximate controllability of the semilinear functional differential equations with unbounded delays. We will also establish the regularity of the solution of the given system. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system by using degree theory. Finally, a simple example to which our main result can be applied is given.

CONTROLLABILITY FOR SEMILINEAR FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

This paper deals with the regularity properties for a class of semilinear integrodierentia l functional dierential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given. Let H and V be two complex Hilbert spaces such that V is a dense subspace of H. Identifying the antidual of H with H we may consider V ‰ H ‰ V ⁄ . In this paper we deal with the approximate controllability for the semilinear equation in H as follows. (SE) ( d dt x(t) = Ax(t) + R t 0 k(t i s)g(s,x(s),u(s))ds + Bu(t),

Regular problem for solutions of a retarded semilinear differential nonlocal equation

Abstract This paper deals with the regularity and existence of solutions of a retarded semilinear differential equation with nonlocal condition by using the fundamental solution in the case where the principal operators are unbounded operators.

Time Optimal Control of Semilinear Control Systems Involving Time Delays

This paper investigates the time optimal control problem to a target set for semilinear control systems involving time delays or memories when a principal operator is unbounded by the construction of a fundamental solution and an easy consequence of the definition of real interpolation spaces. A convergence theorem of time optimal controls for the given semilinear retarded system to a point target set is also given.

Existence of periodic solutions for delayevolution integrodifferential equations

In this paper, we will study the existence of periodic solutions for the delay evolutionintegrodifferential equations in a general Banach space with unbounded operator.

Optimal Control Problems for Evolution Equations of Parabolic Type with Nonlinear Perturbations

In this paper, we study the optimal control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under Lipschitz continuity condition of the nonlinear term, we can obtain the optimal conditions and maximal principles for a given equation, which are described by the adjoint state corresponding to the given equation without the rigorous conditions for the nonlinear term.

Approximate controllability and regularity for nonlinear differential equations

In this article, we deal with the existence, uniqueness, and a variation of solutions of the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator. Moreover, the approximate controllability for the given nonlinear control system is studied.

Controllability for Variational Inequalities of Parabolic Type with Nonlinear Perturbation

We deal with the approximate controllability for the nonlinear functional differential equation governed by the variational inequality in Hilbert spaces and present a general theorems under which previous results easily follow. The common research direction is to find conditions on the nonlinear term such that controllability is preserved under perturbation.

Energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions

In this paper we consider the energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions. Motivated by results of Gerbi and Said-houari (2011, 2008), Li and Zhao (2011), Liu and Chen (2016), Wu etal. (2010) and Lu etal. (2011) we intend to study the energy decay rates for problem (1.1)(1.6). By using the perturbed energy method and Riemannian geometry method, we obtained general energy decay rates

Controllability for nonlinear evolution equations with monotone operators

In this paper, we investigate the approximate controllability for nonlinear evolution equations with monotone operators and nonlinear controllers according to monotone operator theory. We also give the regularity for the nonlinear equation. Finally, an example, to which our main result can be applied, is given.MSC:35F25, 93C20.