On an iterative method for approximate solutions of a generalized Boussinesq model

An iterative method is proposed for nding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature dependent viscosity and thermal conductivity. Under certain conditions, it is proved that such approximate solutions converge to a solution of the original problem; moreover, convergence-rate bounds for the constructed approximate solutions are also obtained

Optimal control problem for the generalized bioconvective flow

In this work, we consider an optimal control problem for the generalized bioconvective flow, which is a well known model to describe the convection caused by the concentration of upward swimming microorganisms in a fluid. Firstly, we study the existence and uniqueness of weak solutions for this model, moreover we prove the existence of the optimal control and we establish the minimum principle by using Dubovitskii-Milyutin’s formalism.DGI-MEC BFM2003- 06446CGCI MECD-DGU Brazil/Spain 117/06FONDECYT 103094

Uniform-in-time error estimates for spectral Galerkin approximations of a mass diffusion model

The goal of this paper is to present uniform-in-time error estimates by considering spectral Galerkin approximations of the Kazhikhov-Smagulov model for strong solutions. To be more precise, we derive an optimal uniform-in-time error bound in the boldsymbol{H}^1\times H^2$ norm for the velocity and density approximations being stated in Theorem 6.Ministerio de Educación y Ciencia MTM2006-0793