The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation
Shaoyong Lai  Department of Applied Mathematics, Southwest Jiaotong University, 610066, Chengdu, China (email) Abstract: In this paper, we consider the solution of an initial value problem for the generalized damped Boussinesq equation $ u_{t t}  a u_{t t x x} 2 b u_{t x x} =  c u_{x x x x}+ u_{x x}  p^2 u + \beta(u^2)_{x x}, $ where $x\in R^1,$ $t > 0,$ $a ,$ $b$ and $c $ are positive constants, $p \ne 0,$ and $\beta \in R^1$. For the case $a + c > b^2$ corresponding to damped oscillations with an infinite number of oscillation cycles, we establish the wellposedness theorem of the global solution to the problem and derive a large time asymptotic solution.
Keywords: Asymptotic solution, wellposedness, Boussinesq equation.
Received: April 2002; Revised: February 2003; Published: May 2003. 
2014 5year IF.957
