Long time well-posedness of Whitham–Boussinesq systems

Fermi-Dirac-Fokker-Planck Equation: Well-posedness & Long-time Asymptotics

A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uni...

Well-posedness of Hybrid Systems

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

Well-Posedness and Long Time Behavior for a Class of Fluid-Plate Interaction Models

We deal with well-posedness and asymptotic dynamics of a class of coupled systems consisting of linearized 3D Navier–Stokes equations in a bounded domain and a classical (nonlinear) elastic plate/shell equation. We consider three models for plate/shell oscillations: (a) the model which accounts for transversal displacement of a flexible flat part of the boundary only, (b) the model for in-plane...

Well-posedness and Long Time Behavior of a Parabolic-hyperbolic Phase-field System with Singular Potentials

In this article, we study the long time behavior of a phase-field parabolichyperbolic system arising from the phase-field theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter. The latter is a singular perturbation ...