Displaying similar documents to “Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary”

Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids

G. Ströhmer, W. Zajączkowski (1999)

Applicationes Mathematicae

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Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.

Unilateral dynamic contact of von Kármán plates with singular memory

Igor Bock, Jiří Jarušek (2007)

Applications of Mathematics

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The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem.

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.