## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

KRM

A recent application of the kinetic theory for many particle systems
is the description of the redistribution of wealth among trading agents in a simple market economy.
This paper provides an analytical investigation of
the particular model with

*quenched saving propensities*, which has been introduced by Chakrabarti, Chatterjee and Manna [11]. We prove uniqueness and dynamical stability of the stationary solution to the underlying Boltzmann equation, and provide estimates on the rate of equilibration. As one main result, we obtain that realistic steady wealth distributions with Pareto tail are only algebraically stable in this framework.
DCDS-B

We propose a method for numerical integration of Wasserstein gradient flows
based on the classical minimizing movement scheme.
In each time step, the discrete approximation is obtained as the solution
of a constrained quadratic minimization problem on a finite-dimensional function space.
Our method is applied to the nonlinear fourth-order Derrida-Lebowitz-Speer-Spohn equation,
which arises in quantum semiconductor theory.
We prove well-posedness of the scheme and derive a priori estimates on the discrete solution.
Furthermore, we present numerical results which indicate
second-order convergence and unconditional stability of our scheme.
Finally, we compare these results to those
obtained from different semi- and fully implicit finite difference discretizations.

JCD

We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a discretized Fokker-Planck equation. For numerical implementation, we employ spectral collocation methods and an exponential time differentiation scheme. We experimentally compare our approach with the more classical method by Ulam that is based on discretization of the transfer operator of the unperturbed flow.

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