OS Partielle Differentialgleichungen: The Cauchy problem for the Jordan-Moore-Gibson-Thompson equation
Time
Thursday, 4. February 2021
15:15 - 16:45
Location
Videokonferenz
Organizer
Speaker:
Prof. Dr. Reinhard Racke
Abstract: We consider the Cauchy problem of a third order in time nonlinear equation known as the JordanMoore-Gibson-Thompson equation arising in acoustics as an alternative model to the Kuznetsov equation. We show a local existence result in appropriate function spaces, and, using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, polynomial decay rates in time for a norm related to the solution will be obtained.