1,065 research outputs found
A Rosenau-type approach to the approximation of the linear Fokker--Planck equation
{The numerical approximation of the solution of the Fokker--Planck equation
is a challenging problem that has been extensively investigated starting from
the pioneering paper of Chang and Cooper in 1970. We revisit this problem at
the light of the approximation of the solution to the heat equation proposed by
Rosenau in 1992. Further, by means of the same idea, we address the problem of
a consistent approximation to higher-order linear diffusion equations
Spectral Dynamics of the Velocity Gradient Field in Restricted Flows
We study the velocity gradients of the fundamental Eulerian equation,
, which shows up in different contexts
dictated by the different modeling of 's. To this end we utilize a basic
description for the spectral dynamics of , expressed in terms of the
(possibly complex) eigenvalues, , which are shown to
be governed by the Ricatti-like equation .
We address the question of the time regularity of four prototype models
associated with different forcing . Using the spectral dynamics as our
essential tool in these investigations, we obtain a simple form of a critical
threshold for the linear damping model and we identify the 2D vanishing
viscosity limit for the viscous irrotational dusty medium model. Moreover, for
the -dimensional restricted Euler equations we obtain global
invariants, interesting for their own sake, which enable us to precisely
characterize the local topology at breakdown time, extending previous studies
in the -dimensional case. Finally, as a forth model we introduce the
-dimensional restricted Euler-Poisson (REP)system, identifying a set of
global invariants, which in turn yield (i) sufficient conditions for
finite time breakdown, and (ii) characterization of a large class of
2-dimensional initial configurations leading to global smooth solutions.
Consequently, the 2D restricted Euler-Poisson equations are shown to admit a
critical threshold
Hyperbolic Balance Laws with a Non Local Source
This paper is devoted to hyperbolic systems of balance laws with non local
source terms. The existence, uniqueness and Lipschitz dependence proved here
comprise previous results in the literature and can be applied to physical
models, such as Euler system for a radiating gas and Rosenau regularization of
the Chapman-Enskog expansion.Comment: 26 page
Large-time Behavior of the Solutions to Rosenau Type Approximations to the Heat Equation
In this paper we study the large-time behavior of the solution to a general
Rosenau type approximation to the heat equation, by showing that the solution
to this approximation approaches the fundamental solution of the heat equation
at a sub-optimal rate. The result is valid in particular for the central
differences scheme approximation of the heat equation, a property which to our
knowledge has never been observed before.Comment: 20 page
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