Spatial and Time Localization of Solutions of the Boussinesq System with211 Nonlinear Thermal Diffusion. Modelling, Analysis and Simulation

摘要

The Boussinesq system arises in Fluid Mechanics when motion is governed by211u001edensity gradients caused by temperature or concentration differences. In this 211u001epaper, we show that, for certain types of nonlinearities in the diffusion term of 211u001ethe heat equation, solutions of Boussinesq system can exhibit two kinds of 211u001ebehaviors: the finite speed of propagation of the support and the extinction in 211u001efinite time, both for the temperature component. Because of the lack of a 211u001ecomparison principle, we use energy methods to proof the occurrence of these 211u001eproperties.