Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation

TL;DR

This paper investigates the long-term behavior of solutions to a Boussinesq-type equation modeling surface waves, establishing existence and asymptotic properties under small initial conditions using contraction mapping.

Contribution

It provides new results on the global existence and asymptotic behavior of solutions for a dissipative Boussinesq-type equation with small initial data.

Findings

Existence of global solutions under small initial conditions

Asymptotic decay properties of solutions

Solutions exist in time weighted spaces

Abstract

We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle.