Instabilities in a reaction diffusion model: spatially homogeneous and distributed systems.
Instability of the stationary solutions of generalized dissipative Boussinesq equation
In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.