Global branching for discontinuous problems
Global Caccioppoli-type and Poincaré inequalities with Orlicz norms.
Global Classical Solutions of Nonlinear Wave Equations.
Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems
In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a solution and its stability with certain small initial and boundary data.
Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
Global dynamics of a reaction-diffusion system.
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 of solutions for a completely coupled Fujita type system of reaction-diffusion equations
We examine the parabolic system of three equations - Δu = , - Δv = , - Δw = , x ∈ , t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
Global existence and blow-up analysis for some degenerate and quasilinear parabolic systems.
Global existence and blow-up for a completely coupled Fujita type system
The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form
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.)