R. A. Capistrano-Filho, F. A. Gallego, A. F. Pazoto
Published 2017-12-22Version 1
A family of Boussinesq systems has been proposed in P. J. Olver, Hamiltonian and non-Hamiltonian models for water waves. Lecture Notes in Physics, vol.195, Springer Verlag, (1984), 273-296, to describe the bi-directional propagation of small amplitude long waves on the surface of shallow water. In this paper, we investigate the boundary stabilization of the generalized higher order Boussinesq systems of KdV--type posed on a interval. We design a two-parameter family of feedback laws for which the solutions are globally defined in time and exponentially decreasing in the energy space.
Large time behavior of solutions to a dissipative Boussinesq system
Some results on the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
Large time behavior of solutions of the heat equation with inverse square potential
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