Jum-Ran Kang

Controllability of the second-order differential inclusion in Banach spaces

Abstract The purpose of this paper is to study the controllability for the second-order differential inclusion in Banach spaces. We rely on a fixed point theorem for condensing maps due to Martelli. We consider the damping term x′(·) and find a control u such that the solution satisfies x(T)=x1 and x′(T)=y1.

Energy decay rates for von Kármán system with memory and boundary feedback

Abstract In this paper we study the von Karman plate model with long-range memory and boundary nonlinear feedback. We establish an explicit and general decay rate result, using some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function.

General decay for Kirchhoff plates with a boundary condition of memory type

In this paper we consider Kirchhoff plates with a memory condition at the boundary. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.MSC:35B40, 74K20, 35L70.

Pullback attractors for the non-autonomous coupled suspension bridge equations

In this paper, we consider the pullback D-attractors for the non-autonomous coupled suspension bridge equations when external terms are unbounded in a phase space.

Global attractors for the suspension bridge equations with nonlinear damping

In this paper, we prove the existence of a global attractor for the suspension bridge equations with nonlinear damping.

Long-time behavior of a suspension bridge equations with past history

In this paper, we study a suspension bridge equation with memory effects. For the suspension bridge equation without memory, there are many classical results. Existing results mainly devoted to existence and uniqueness of a weak solution, energy decay of solution and existence of global attractors. However the existence of global attractors for the suspension bridge equation with memory was no yet considered. The object of the present paper is to provide some results on the well-posedness and long-time behavior to the suspension bridge equation when the unique damping mechanism is given by the memory term.

GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY

Abstract In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

Asymptotic stability of a viscoelastic problem with Balakrishnan–Taylor damping and time-varying delay

A viscoelastic problem with BalakrishnanTaylordamping and time-varying delay of the form utt(a+bu2+(u,ut))u+0tg(ts)u(s)ds+1f1(ut(x,t))+2f2(ut(x,t(t)))=0is considered. We prove a general stability result for the equation without the condition 2>0 by establishing some Lyapunov functionals which are equivalent to the energy of the equation instead of multiplier technique and using some properties of convex functions.

Global nonexistence of solutions for von Karman equations with variable exponents

Abstract We consider the von Karman equations with variable exponents: u t t + Δ 2 u + a | u t | m ( ⋅ ) − 2 u t = [ u , F ( u ) ] + b | u | p ( ⋅ ) − 2 u where a and b are positive constants and the exponents m ( ⋅ ) and p ( ⋅ ) are given measurable functions. There are many literatures on the blow-up result of solutions for the wave equation. However, to the best of our knowledge, there is no blow-up result of solutions for von Karman equations. We investigate a finite time blow-up result of solutions with nonpositive initial energy as well as positive initial energy.

Blow-up results for viscoelastic wave equations with weak damping

Abstract In this work we consider a viscoelastic wave equation of the form u t t − Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + h ( u t ) = | u | p − 2 u with Dirichlet boundary condition. There are much literature on the blow-up result of solutions for the wave equation with damping term having polynomial growth near zero. However, to my knowledge, there is no blow-up result of solutions for the viscoelastic wave equation without polynomial growth near zero assumption on the damping term. This work is devoted to study a finite time blow-up result of solution with nonpositive initial energy as well as positive initial energy without imposing any restrictive growth near zero assumption on the damping term.