Displaying similar documents to “Attractor for a viscous coupled Camassa-Holm equation.”

Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul Park, Sun Hye Park (2006)

Czechoslovak Mathematical Journal

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We consider the damped semilinear viscoelastic wave equation u ' ' - Δ u + ∫ 0 t h ( t - τ ) div { a ∇ u ( τ ) } d τ + g ( u ' ) = 0 in Ω × ( 0 , ∞ ) 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.

Global and exponential attractors for a Caginalp type phase-field problem

Brice Bangola (2013)

Open Mathematics

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We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.