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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.

Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²

Agnieszka Herczak, Michał Olech (2009)

Banach Center Publications

We investigate a system describing electrically charged particles in the whole space ℝ². Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions.

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

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