We consider the Cauchy problem for the n-dimensional generalized damped Boussinesq equation. Based on decay estimates of solutions to the corresponding linear equation, we define a solution space with time weighted norms. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in the corresponding Sobolev spaces are established by the contraction mapping principle.
Submitted May 31, 2012. Published June 10, 2012.
Math Subject Classifications: 35L30, 35L75.
Key Words: Generalized damped equation; global solution; asymptotic behavior.
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| Yinxia Wang |
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power
Zhengzhou 450011, China
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