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Article

Esfahani, Amin
Instability of the stationary solutions of generalized dissipative Boussinesq equation. (English). Applications of Mathematics, vol. 59 (2014), issue 3, pp. 345-358
MSC: 35B35, 35Q35, 35Q53, 76B15 | MR 3232635 | Zbl 06362231 | DOI: 10.1007/s10492-014-0059-1
Keywords:
damped Boussinesq equation; stationary solution; instability
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.
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