Jordan--Moore--Gibson--Thompson equation is a model equation arising in acoustics as an alternative model to the well-known Kuznetsov equation.
In this talk, we established the local existence, global existence and decay rate of the solution of the full nonlinear problem JMGT equation.
First, using the contraction mapping theorem, we show a local existence result in appropriate function spaces. Second, by using the energy method together with a bootstrap argument, we prove a global existence result for small data without using the linear decay. Third, polynomial decay rates in time for the solution is obtained.