P. Braz e Silva

Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system

This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k. As k → ∞, the authors obtain the damped von Kármán model with associated energy exponentially decaying to zero as well.

On the behavior of Kazhikov-Smagulov mass diffusion model for vanishing diffusion and viscosity coefficients

We consider the motion of a viscous incompressible fluid consisting of two components with a diffusion effect obeying Fick’s law in ℝ3. We prove that there exists a small time interval where the fluid variables converge uniformly as the viscosity and the diffusion coefficient tend to zero. In the limit, we find a non-homogeneous, non-viscous, incompressible fluid governed by an Euler-like system.