Abstract
In this paper, we investigate the initial boundary value problem for the linearized double dispersion equation on the half space \begin{document}$\mathbb{R}^{n}_{+}$\end{document} . We convert the initial boundary value problem into the initial value problem by odd reflection. The asymptotic profile of solutions to the initial boundary value problem is derived by establishing the asymptotic profile of solutions to the initial value problem. More precisely, the asymptotic profile of solutions is associated with the convolution of the partial derivative of the fundamental solutions of heat equation and the fundamental solutions of free wave equation.
Highlights
The following double dispersion equation wtt − wxx = 1xx. (1)is derived by using the Hamilton principle in the study of the nonlinear wave propagation in waveguide
We investigate the initial boundary value problem for the linearized equation of the generalized double dispersion equation (3) on the half space Rn+ = {x|xn > 0}(n ≥ 1)
The nonlinear approximation result of global solutions to one dimensional double dispersion equation is established by Kato, Wang and Kawashima [8]
Summary
We refer to (see [13] and [14])
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