Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation

Abstract EN

We investigate the Cauchy problem for the generalized damped Boussinesq equation.

Under small condition on the initial value, we prove the global existence and optimal decay estimate of solutions for all space dimensions n≥1.

Moreover, when n≥2, we show that the solution can be approximated by the linear solution as time tends to infinity.