Decay in the one dimensional generalized improved Boussinesq equation.

Abstract: The purpose of this talk is to explain the decay problem for the generalized improved (or regularized)  Boussinesq model with power type nonlinearity, a modification of the originally ill-posed shallow water waves model derived by Boussinesq.

The associated decay problem has been studied by Liu, and more recently by Cho-Ozawa, showing scattering in weighted spaces provided the power of the nonlinearity $p$ is sufficiently large. In this talk we remove that condition on the power $p$ and prove decay to zero in terms of the energy space norm $L^2\times H^1$, for any $p>1$, in two almost complementary regimes:  (i) outside the light cone for all small, bounded in time  $H^1\times H^2$ solutions, and (ii) decay on compact sets of arbitrarily large bounded in time $H^1\times H^2$ solutions.

These works were developed in collaboration with C. Muñoz.

Date: Oct 09, 2019 at 17:00:00 h
Venue: Beauchef 851, Torre Norte, 5to Piso. Sala de Seminarios Seminario Felipe Álvarez Daziano
Speaker: Christopher Maulén
Affiliation: Universida de Chile
Coordinator: Matteo Rizzi

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