Displaying similar documents to “Global solutions for a nonlinear wave equation with the p -Laplacian operator.”

Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul Park, Sun Hye Park (2006)

Czechoslovak Mathematical Journal


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.

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


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.

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

Brice Bangola (2013)

Open Mathematics


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.