EuDML | Browse

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...

Displaying 21 – 36 of 36

Global infinite energy solutions of the critical semilinear wave equation.

Global Instability and Essential Spectrum in Semilinear Evolution Equations.

Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.

Global Solution of the System of Wave and Klein-Gordon Equations.

Global solutions for a nonlinear hyperbolic equation with boundary memory source term.

Global solutions for a nonlinear wave equation with the $p$ -Laplacian operator.

Global solutions of the equations of elastodynamics for incompressible materials.

Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity [Book]

Global solvability for the degenerate Kirchhoff equation

Global solvability to the Kirchhoff equation for a new class of initial data.

Global sound waves for quasilinear second order wave equations.

Global stability of travelling fronts for a damped wave equation with bistable nonlinearity

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

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

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

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

Currently displaying 21 – 36 of 36