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.
Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain.
Global existence of smooth solutions for the compressible viscous fluid flow with radiation in
This paper is concerned with the 3-D Cauchy problem for the compressible viscous fluid flow taking into account the radiation effect. For more general gases including ideal polytropic gas, we prove that there exists a unique smooth solutions in , provided that the initial perturbations are small. Moreover, the time decay rates of the global solutions are obtained for higher-order spatial derivatives of density, velocity, temperature, and the radiative heat flux.
Global existence, uniqueness, and asymptotic behavior of solution for -Laplacian type wave equation.
Global existence versus blow up for some models of interacting particles
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.
Global pointwise a priori bounds and large time behaviour for a nonlinear system describing the spread of infectious disease
This paper considers a reaction-diffusion system with biatic diffusion.Existence of a globally bounded solution is proved and its large timebehaviour is given.
Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.
Global solutions and finite time blow up for damped semilinear wave equations
Global solutions and quenching to a class of quasilinear parabolic equations.
Global solutions for a nonlinear hyperbolic equation with boundary memory source term.
Global solutions for a nonlinear wave equation with the -Laplacian operator.
Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations.
Global stability of travelling fronts for a damped wave equation with bistable nonlinearity
We consider the damped wave equation on the whole real line, where is a bistable potential. This equation has travelling front solutions of the form which describe a moving interface between two different steady states of the system, one of which being the global minimum of . We show that, if the initial data are sufficiently close to the profile of a front for large , the solution of the damped wave equation converges uniformly on to a travelling front as . The proof of this global stability...
Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.