Blow-Up Of Solutions For The Damped Boussinesq Equation

Abstract

We consider the blow-up of solutions as a function of time to the initial boundary value problem for the damped Boussinesq equation. Under some assumptions we prove that the solutions with vanishing initial energy blow up in finite time

Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation

“…The generalization of Boussinesq equation was studied in numerous papers [3,4,6,9,12,13,15,16,27,28]. Liu [12,13] studied the instability of solitary waves for a generalized Boussinesq type equation…”

“…(1.8) in two space dimensions. Polat et al [15] established the blow-up of the solutions for the initial-boundary value problem of the damped Boussinesq equation…”

Existence, global nonexistence, and asymptotic behavior of solutionsfor the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation

“…Polat et al [8] established the blow up of the solution for the initial boundary value problem of the damped Boussinesq equation…”

“…Varlamov [12] investigated the long-time behavior of solutions to initial value, spatially periodic, and initial-boundary value problems for equation (1.3) in 2 space dimensions. Polat et al [8] established the blow up of the solution for the initial boundary value problem of the damped Boussinesq equation…”

The long time behavior of solutions for a

“…Making use of the eigenfunction expansion method in a ball, Varlamov [8] investigated a long time asympotics of solution for a Boussinesq equation similar to equation (2). Polat [11] considered the blow up phenomena of solutions for the following Boussinesq equation with damping term…”