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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 regularity of solutions for complex Ginzburg-Landau equations

Stéphane Descombes, Mohand Moussaoui (2000)

Bollettino dell'Unione Matematica Italiana

Si considerano equazioni di Ginzburg-Landau complesse del tipo $u_{t} - α Δ u + P ({|u|}^{2}) u = 0$ in $R^{N}$ dove $P$ è polinomio di grado $K$ a coefficienti complessi e $α$ è un numero complesso con parte reale positiva $ℜ α$ . Nell'ipotesi che la parte reale del coefficiente del termine di grado massimo $P$ sia positiva, si dimostra l'esistenza e la regolarità di una soluzione globale nel caso $|α| < C ℜ α$ , dove $C$ dipende da $K$ e $N$ .

Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents

Aya Khaldi, Amar Ouaoua, Messaoud Maouni (2022)

Mathematica Bohemica

We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms $u_{t} - M (\int_{Ω} {| \nabla u |}^{2} d x) Δ u + {| u |}^{m (x) - 2} u_{t} = {| u |}^{r (x) - 2} u .$ We prove with suitable assumptions on the variable exponents $r (\cdot),$ $m (\cdot)$ the global existence...

Global existence and stability of some semilinear problems

Mokhtar Kirane, Nasser-eddine Tatar (2000)

Archivum Mathematicum

We prove global existence and stability results for a semilinear parabolic equation, a semilinear functional equation and a semilinear integral equation using an inequality which may be viewed as a nonlinear singular version of the well known Gronwall and Bihari inequalities.

Global existence and uniform stabilization of a nonlinear Timoshenko beam.

Ammari, Kais (2002)

Portugaliae Mathematica. Nova Série

Global existence and uniqueness of weak solutions to Cahn-Hilliard-Gurtin system in elastic solids

Irena Pawłow, Wojciech M. Zajączkowski (2008)

Banach Center Publications

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 a quasilinear wave equation outside of star-shaped domains

Hart F. Smith (2001)

Journées équations aux dérivées partielles

This talk describes joint work with Chris Sogge and Markus Keel, in which we establish a global existence theorem for null-type quasilinear wave equations in three space dimensions, where we impose Dirichlet conditions on a smooth, compact star-shaped obstacle $𝒦 \subset ℝ^{3}$ . The key tool, following Christodoulou [1], is to use the Penrose compactification of Minkowski space. In the case under consideration, this reduces matters to a local existence theorem for a singular obstacle problem. Full details will...

Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain (2011)

Annales de l’institut Fourier

Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.

Global existence for nonlinear system of wave equations in 3-D domains

Jianwei Yang (2011)

Applicationes Mathematicae

We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.

Global existence for quasi-linear dissipative hyperbolic equations with large data and small parameter

Albert J. Milani (1990)

Czechoslovak Mathematical Journal

Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.

Albert J. Milani (1988)

Mathematische Zeitschrift

Global existence for the nonlinear equations of crystal optics

Otto Liess (1989)

Journées équations aux dérivées partielles

Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data

C. Bardos, P. Degond (1985)

Annales de l'I.H.P. Analyse non linéaire

Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain.

Nakao Hayashi (1993)

Manuscripta mathematica

Global existence of smooth solutions for the compressible viscous fluid flow with radiation in $ℝ^{3}$

Hyejong O, Hakho Hong, Jongsung Kim (2023)

Applications of Mathematics

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 $[0, \infty)$ , 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 of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions

Pierre Degond (1986)

Annales scientifiques de l'École Normale Supérieure

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