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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 strong solutions for the magnetohydrodynamic equations.

Zhang, Jianwen (2008)

Boundary Value Problems [electronic only]

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 nonlinear Schroedinger–Chern–Simons system on a surface

Sophia Demoulini (2007)

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

Global existence for a one-dimensional model in gas dynamics

Serge Njamkepo (1997)

Applicationes Mathematicae

We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.

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 a Riccati equation arising in a boundary control problem for distributed parameters

Franco Flandoli (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

Tomáš Bárta (2013)

Open Mathematics

We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.

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 degenerate quadratic reaction-diffusion systems

M. Pierre, R. Texier-Picard (2009)

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

Global existence for functional semilinear integro-differential equations

Sotiris K. Ntouyas (1998)

Archivum Mathematicum

In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.

Global existence for non-linear partial differential equations of the first order

A. Adamus-Kulczycka (1973)

Annales Polonici Mathematici

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