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
“…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…”
Section: Eq (14) Is Called Improved Boussinesq Equation (Ibq Equatimentioning
confidence: 99%
“…(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…”
Section: Eq (14) Is Called Improved Boussinesq Equation (Ibq Equatimentioning
We consider the existence, both locally and globally in time, and the blow-up of solutions for the Cauchy problem of 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…”
Section: Eq (14) Is Called Improved Boussinesq Equation (Ibq Equatimentioning
confidence: 99%
“…(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…”
Section: Eq (14) Is Called Improved Boussinesq Equation (Ibq Equatimentioning
We consider the existence, both locally and globally in time, and the blow-up of solutions for the Cauchy problem of the generalized damped multidimensional Boussinesq equation.
“…Polat et al [8] established the blow up of the solution for the initial boundary value problem of the damped Boussinesq equation…”
Section: Introductionmentioning
confidence: 99%
“…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…”
We consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.
“…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…”
The initial-boundary value problem is investigated for a generalized Boussinesq equation with the quadratic nonlinearity. For small initial data and homogeneous boundary conditions, its solution is constructed in the form of a series which converges absolutely and uniformly. The long time asymptotic expansion of the solution is acquired to show the nonlinear effects of amplitude.
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