Existence and asymptotic behaviour of solutions of a nonlinear evolution problem
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where is the pseudo-Laplacian operator.
Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in
Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
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.
Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²
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 attractivity results for a class of degenerate functional-parabolic problems
Existence and attractors of solutions for nonlinear parabolic systems.
Existence and bifurcation for some elliptic problems on exterior strip domains.
Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients.
Existence and boundary stabilization of the semilinear Mindlin-Timoshenko system.
Existence and decay of solutions of some nonlinear parabolic variational inequalities.
Existence and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks on time scales.
Existence and limiting behaviour for damped nonlinear evolution equations with nonlocal terms
Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
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.
Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term
We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as by applying the Lyapunov method.
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary.
Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms
We consider the existence, both locally and globally in time, the decay and the blow up of the solution for the extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution by Banach contraction mapping principle. The decay estimates of the solution are proved by using Nakao’s inequality. Moreover, under suitable conditions on the initial datum, we prove that the solution blow up in finite time.