113 research outputs found
Well-posedness of the initial value problem for the Ostrovsky-Hunter equation with spatially dependent flux
In this paper we study the Ostrovsky-Hunter equation for the case where the
flux function may depend on the spatial variable with certain
smoothness. Our main results are that if the flux function is smooth enough
(specified later), then there exists a unique entropy solution. To show the
existence, after proving some a priori estimates we have used the method of
compensated compactness and to prove the uniqueness we have employed the method
of doubling of variables
On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions
We analyze upwind difference methods for strongly degenerate
convection-diffusion equations in several spatial dimensions. We prove that the
local -error between the exact and numerical solutions is
, where is the spatial dimension and
is the grid size. The error estimate is robust with respect to
vanishing diffusion effects. The proof makes effective use of specific kinetic
formulations of the difference method and the convection-diffusion equation
An explicit finite difference scheme for the Camassa-Holm equation
We put forward and analyze an explicit finite difference scheme for the
Camassa-Holm shallow water equation that can handle general initial data
and thus peakon-antipeakon interactions. Assuming a specified condition
restricting the time step in terms of the spatial discretization parameter, we
prove that the difference scheme converges strongly in towards a
dissipative weak solution of Camassa-Holm equation.Comment: 45 pages, 6 figure
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