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We consider the damped wave equation $α u_{t t} + u_{t} = u_{x x} - V^{'} (u)$ on the whole real line, where $V$ is a bistable potential. This equation has travelling front solutions of the form $u (x, t) = h (x - s t)$ which describe a moving interface between two different steady states of the system, one of which being the global minimum of $V$ . We show that, if the initial data are sufficiently close to the profile of a front for large $| x |$ , the solution of the damped wave equation converges uniformly on $ℝ$ to a travelling front as $t \to + \infty$ . The proof of this global stability...

Global weak solutions for $1 + 2$ dimensional wave maps into homogeneous spaces

Yi Zhou (1999)

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

Global weak solutions of the wave map system to compact homogeneous spaces.

A. Freiere (1996)

Manuscripta mathematica

Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay

Houssem Eddine Khochemane, Sara Labidi, Sami Loucif, Abdelhak Djebabla (2025)

Mathematica Bohemica

We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism...

Global well-posedness for two-dimensional semilinear wave equations.

Fonseca, Germán E. (2000)

Revista Colombiana de Matemáticas

Globally regular solutions to the $u^{5}$ Klein-Gordon equation

Michael Struwe (1988)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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