Existence and asymptotic behavior of global solutions for a class of nonlinear higher-order wave equation.
The present paper studies the existence and uniqueness of global solutions and decay rates to a given nonlinear hyperbolic problem.
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where is the pseudo-Laplacian operator.
We consider the damped semilinear viscoelastic wave equation 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.
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.
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.