The growth or decay estimates for nonlinear wave equations with damping and source terms
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Published on: February 13, 2018
Peng Zeng1, Dandan Li1, Yuanfei Li1
1School of Data Science, Guangzhou Huashang College, Guangdong 511300, China.
Abstract:
The spatial decay or growth behavior of a coupled nonlinear wave equation with damping and source terms is considered. By defining the wave equations in a cylinder or an exterior region, the spatial growth and decay estimates for the solutions are obtained by assuming that the boundary conditions satisfy certain conditions. We also show that the growth or decay rates are faster than those obtained by relevant literature. This kind of spatial behavior can be extended to a nonlinear system of viscoelastic type. In the case of decay, we also prove that the total energy can be bounded by known data.
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