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Start Over Creator Park, Jong Yeoul

1. Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Creator:
Park, Jong Yeoul and Park, Sun Hye
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
asymptotic stability, viscoelastic problems, boundary dissipation, and wave equation
Language:
English
Description:
We consider the damped semilinear viscoelastic wave equation \[ u^{\prime \prime } - \Delta u + \int ^t_0 h (t-\tau ) \div \lbrace a \nabla u(\tau ) \rbrace \mathrm{d}\tau + g(u^{\prime }) = 0 \quad \text{in}\hspace{5.0pt}\Omega \times (0,\infty ) \] with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On solutions of quasilinear wave equations with nonlinear damping terms

Creator:
Park, Jong Yeoul and Bae, Jeong Ja
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
quasilinear wave equation, existence and uniqueness, asymptotic behavior, and Galerkin method
Language:
English
Description:
In this paper we consider the existence and asymptotic behavior of solutions of the following problem: \[ u_{tt}(t,x)-(\alpha +\beta \Vert \nabla u(t,x)\Vert _2^2 +\beta \Vert \nabla v(t,x)\Vert _2^2)\Delta u(t,x) +\delta |u_t(t,x)|^{p-1}u_t(t,x) \quad =\mu |u(t,x)|^{q-1}u(t,x), \quad x \in \Omega ,\quad t \ge 0, v_{tt}(t,x)-(\alpha +\beta \Vert \nabla u(t,x)\Vert _2^2+ \beta \Vert \nabla v(t,x)\Vert _2^2) \Delta v(t,x) +\delta |v_t(t,x)|^{p-1}v_t(t,x) \quad =\mu |v(t,x)|^{q-1}v(t,x), \quad x \in \Omega ,\quad t \ge 0, u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x), \quad x \in \Omega , v(0,x)=v_0(x),\quad v_t(0,x)=v_1(x), \quad x \in \Omega , u|_{_{\partial \Omega }}=v|_{_{\partial \Omega }}=0 \] where $q > 1$, $ p \ge 1$, $ \delta >0$, $ \alpha > 0$, $ \beta \ge 0 $, $\mu \in \mathbb R $ and $\Delta $ is the Laplacian in $\mathbb R^N$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Optimization and identification of nonlinear uncertain systems

Creator:
Park, Jong Yeoul, Kang, Jong Han, and Jung, Il Hyo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
optimal control, Galerkin method, nonlinear systems, identification problem, and necessary condition
Language:
English
Description:
In this paper we consider the optimal control of both operators and parameters for uncertain systems. For the optimal control and identification problem, we show existence of an optimal solution and present necessary conditions of optimality.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary

Creator:
Park, Jong Yeoul and Park, Sun Hye
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
existence of solution, differential inclusion, memory source term, and uniform decay
Language:
English
Description:
We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public