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Stability in thermoelasticity of type III
The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation
| 1. | Department of Applied Mathematics, Southwest Jiaotong University, 610066, Chengdu, China |
| 2. | Department of Mathematics and Statistics, Curtin University of Technology, GOP Box U1987, Perth, WA 6845, Australia |
$ 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 well-posedness theorem of the global solution to the problem and derive a large time asymptotic solution.
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