Article ID Journal Published Year Pages File Type
843805 Nonlinear Analysis: Theory, Methods & Applications 2009 11 Pages PDF
Abstract

The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in an elastic waveguide model utt−Δu−Δutt+Δ2u−Δut−Δg(u)=f(x)utt−Δu−Δutt+Δ2u−Δut−Δg(u)=f(x). It proves that when the space dimension N≤5N≤5, under rather mild conditions the dynamical system associated with the above-mentioned IBVP possesses a global attractor which is connected and has finite fractal and Hausdorff dimension.

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