On a shallow water wave equation
Abstract
The main topic of this thesis is the study of a nonlinear partial differential equation, the Camassa-Holm (CH) equation: ut - utxx + 3uux - 2uxuxx -uuxxx = 0.
Has parts
Holden, Helge; Raynaud, Xavier. Convergence of a finite different scheme for the Camassa-Holm equation. SIAM Journal on Numerical Analysis. 33: 1655-1680, 2006.Holden, Helge; Raynaud, Xavier. A convergent numerical scheme for the Camassa-Holm equation based on multipeakons. Discrete and Continuous Dynamical Systems - Series A. 14(3): 505-523, 2006.
Kalisch, Henrik; Raynaud, Xavier. Convergence of a Spectral Projection of the Camassa-Holm equation. Numerical Methods for Partial Differential Equations. 22(5): 1197-1215, 2006.
Holden, Helge; Raynaud, Xavier. Global conservative multipeakon solutions of the Camassa-Holm equation. Journal of Hyperbolic Differential Equation. 4(1): 39-64, 2007.
Holden, Helge; Raynaud, Xavier. Global conservative solutions of the generalized hyperelastic-rod wave equation.. Journal of Differential Equations. 233: 448-484, 2007.