Instability of the stationary solutions of generalized dissipative Boussinesq equation. (English) Zbl 1340.35257

Summary: 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.


35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
35B35 Stability in context of PDEs
35B44 Blow-up in context of PDEs
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