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Browsing by Author "Kim, J. U."

Now showing 1 - 3 of 3
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    Invariant measures for the tochastic von Karman plate equation
    Kim, J. U. (Siam Publications, 2005)
    We prove the existence of an invariant measure for the von Karman plate equation with random noise. The nonlinear term which symbolizes the von Karman equation inhibits the standard procedure for the existence of an invariant measure. We propose a technically different approach to handle such intricate nonlinear equations.
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    On a stochastic hyperbolic system in linear elasticity
    Kim, J. U. (Siam Publications, 2000-08)
    In this paper we discuss the Cauchy problem for linear elasticity with a space-time white noise forcing term. We show that the solution can be represented by a formula analogous to the Riesz formula for solutions of a wave equation. The solution is a generalized stochastic process and is obtained as the limit of a sequence of ordinary stochastic processes. Our basic tool is the Hilbert space method combined with geometric properties of solutions inherent with a hyperbolic system.
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    On a wave equation with a boundary condition associated with capillary waves
    Kim, J. U. (Siam Publications, 1998-09)
    This paper discusses an initial-boundary value problem for a wave equation with a nonstandard boundary condition associated with linear capillary waves on the surface of a compressible liquid. We prove the well-posedness of this problem. Our main technical device is the Fourier transform.