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(Research report / Forskningsrapport, 2006)
We consider higher-order Camassa--Holm equations describing exponential curves of the manifold of smooth orientation preserving diffeomorphisms of the unit circle in the plane. We establish the existence of a strongly ...
(Research report / Forskningsrapport, 2006)
We suggest a finite dfference scheme for the Camassa-Holm equation that can handle general H1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We ...
(Research report / Forskningsrapport, 2006)
(Research report / Forskningsrapport, 2006)
Recent work [4] has shown that the Degasperis-Procesi equation is well-posed in the class of (discontinuous) entropy solutions. In the present paper we construct numerical schemes and prove that they converge to entropy ...
(Research report / Forskningsrapport, 2005)
(Research report / Forskningsrapport, 2005)
We consider a shallow water equation of Camassa-Holm type, containing nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a ...
(Research report / Forskningsrapport, 2005)
We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa-Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, ...
(Research report / Forskningsrapport, 2004)
We show existence of a unique, regular global solution of the parabolic-elliptic system
$u_t +f(t,x,u)_x+g(t,x,u)+P_x=(a(t,x) u_x)_x$
and $-P_{xx}+P=h(t,x,u,u_x)+k(t,x,u)$ with initial data
$u|_{t=0} = u_0$. Here ...
(Research report / Forskningsrapport, 2004)
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa--Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous ...