38 research outputs found
Entropy decay of discretized fokker-planck equations I—Temporal semidiscretization
AbstractIn this paper, we study the large time behavior of a fully implicit semidiscretization (in time) of parabolic Fokker-Planck type equations. Using logarithmic Sobolev inequalities exponential decay of the relative entropy (w.r.t. the steady state) is proved which yields convergence of the discrete scheme towards the unique steady state. The exponential decay rate recovers as At J 0 the decay rate of the original Fokker-Planck type equations
Strong solutions of the thin film equation in spherical geometry
We study existence and long-time behaviour of strong solutions for the thin
film equation using a priori estimates in a weighted Sobolev space. This
equation can be classified as a doubly degenerate fourth-order parabolic and it
models coating flow on the outer surface of a sphere. It is shown that the
strong solution asymptotically decays to the flat profile
Decay rates for a class of diffusive-dominated interaction equations
We analyse qualitative properties of the solutions to a mean-field equation
for particles interacting through a pairwise potential while diffusing by
Brownian motion. Interaction and diffusion compete with each other depending on
the character of the potential. We provide sufficient conditions on the
relation between the interaction potential and the initial data for diffusion
to be the dominant term. We give decay rates of Sobolev norms showing that
asymptotically for large times the behavior is then given by the heat equation.
Moreover, we show an optimal rate of convergence in the -norm towards the
fundamental solution of the heat equation.Comment: 22 page
A Residual Based Error Formula for a Class of Transport Equations
We present an exact residual based error formula in natural norms for a class of transport equations
A Hybrid Simulation Method for Radivative Transfer Equations
We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role
Numerical evidance for the non-existing of solutions of the equations desribing rotational fiber spinning
Abstract. The stationary, isothermal rotational spinning process of fibers is considered. The investigations are concerned with the case of large Reynolds (± = 3/Re ¿ 1) and small Rossby numbers (\\\" ¿ 1). Modelling the fibers as a Newtonian fluid and applying slender body approximations, the process is described by a two–point boundary value problem of ODEs. The involved quantities are the coordinates of the fiber’s centerline, the fluid velocity and viscous stress. The inviscid case ± = 0 is discussed as a reference case. For the viscous case ± > 0 numerical simulations are carried out. Transfering some properties of the inviscid limit to the viscous case, analytical bounds for the initial viscous stress of the fiber are obtained. A good agreement with the numerical results is found. These bounds give strong evidence, that for ± > 3\\\"2 no physical relevant solution can exist. A possible interpretation of the above coupling of ± and \\\" related to the die–swell phenomenon is given