On some reversibility properties of Hamilton-Jacobi equations

Friday, September 13th 10:30 – 10:55, 2019
WASTE4T Room at DeustoTech

Carlos Esteve
DeustoTech, Bilbao, Basque Country, Spain


We consider a Hamilton-Jacobi equation of the form $u_t+H(t,x,Du)=0$, with some initial datum $u(0,x)=g(x)$. When one solves this problem forward in time, it is a natural question whether or not any information of the initial datum is lost along the time interval $[0,T]$. An approach to this question is to consider the problem backward in time, with terminal condition $u(T,x)$, and see if one recovers the initial datum $g(x)$.