Special Session 98: Control, Inverse problems and Long time dynamics of Evolutionary Systems

Stability for non-autonomous degenerate wave equations.
GENNI FRAGNELLI
University of Siena
Italy
Co-Author(s):    Mohammad Akil, Sarah Ismail
Abstract:
We consider a non-autonomous wave equation on $(0,1)$ with degeneracy at $x = 0$. Obviously, the presence of a non-autonomous term and of a degenerate function leads us to use different spaces with respect to the standard ones and it gives rise to some new difficulties. However, thanks to some suitable assumptions on the functions, one can prove some estimates on the associated energy that are crucial to obtain a uniform exponential decay.