Spectrum of elliptic operators and stability of travelling waves

Article type: Research Article

Authors: Volpert, A.I.^; | Volpert, V.A.

Affiliations: Department of Mathematics, Technion, 32000 Haifa, Israel | Laboratoire d’analyse numérique, Université Lyon I , UMR 5585 CNRS 69622 Villeurbanne Cedex, France

Note: [] Corresponding author. E‐mail: volp@techunix.technion.ac.il.

Abstract: Location of the discrete and continuous spectrum of the operator corresponding to a boundary value problem for an elliptic system of equations in an unbounded cylinder is studied. Stability of multi‐dimensional travelling waves with respect to small perturbations is proved. These results allow us to prove global stability of travelling waves, i.e., that they describe large time asymptotic of solutions of the initial‐boundary value problem for a class of initial conditions, and to obtain a minimax representation for the wave velocity.

Journal: Asymptotic Analysis, vol. 23, no. 2, pp. 111-134, 2000