Global existence and asymptotic behavior of solutions for a class of nonlinear degenerate wave equations.
Global existence and asymptotic behavior of solutions for some nonlinear hyperbolic equation.
Global existence and asymptotic behaviour for a degenerate diffusive SEIR model.
Global existence and blow-up for a shallow water equation
Global existence and convergence of solutions to a cross-diffusion cubic predator-prey system with stage structure for the prey.
Global existence and convergence to steady states in a chemorepulsion system
In this paper we consider a model of chemorepulsion. We prove global existence and uniqueness of smooth classical solutions in space dimension n = 2. For n = 3,4 we prove the global existence of weak solutions. The convergence to steady states is shown in all cases.
Global existence and decay of solutions of a coupled system of BBM-Burgers equations.
The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces Hs(R) x Hs(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm Lq(R) x Lq(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.
Global existence and energy decay of solutions to a Bresse system with delay terms
We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.
Global existence and energy decay of solutions to the Cauchy problem for a wave equation with a weakly nonlinear dissipation.
Global existence and extinction of weak solutions to a class of semiconductor equations with fast diffusion terms.
Global existence and internal nonlinear stabilization of an elasticity system. (Existence globale et stabilisation interne non linéaire d'un système d'élasticité.)
Global existence and estimates of solutions for a quasilinear parabolic system.
Global existence and long-time behavior of solutions to a class of degenerate parabolic equations
We study the global existence and long-time behavior of solutions for a class of semilinear degenerate parabolic equations in an arbitrary domain.
Global existence and nonexistence for semiliniear parabolic systems with nonlinear boundary conditions.
Global existence and nonlinear boundary stabilization of an elastic system. (Existence globale et stabilisation frontière non linéaire d'un système d'élasticité.)
Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping
A viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping is considered. Using integral inequalities and multiplier techniques we establish polynomial decay estimates for the energy of the problem. The results obtained in this paper extend previous results by Tatar and Zaraï [25].
Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents
We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms We prove with suitable assumptions on the variable exponents the global existence...
Global existence and uniform stabilization of a nonlinear Timoshenko beam.
Global existence and uniqueness of weak solutions to Cahn-Hilliard-Gurtin system in elastic solids
In this paper we study the Cahn-Hilliard-Gurtin system describing the phase-separation process in elastic solids. The system has been derived by Gurtin (1996) as an extension of the classical Cahn-Hilliard equation. For a version with viscosity we prove the existence and uniqueness of a weak solution on an infinite time interval and derive an absorbing set estimate.
Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.