# Time-asymptotic Behaviour in Hamilton-Jacobi Equations

Wednesday, November 17, 1999 - 9:30am - 10:20am

Keller 3-180

Jean-Michel Roquejoffre (Université de Toulouse I (Sciences Sociales))

The problem under study is the following Hamilton-Jacobi equation

utH(x,Du)=0

with periodic conditions in x or in a bounded domain with Dirichlet conditions. When H is strictly convex with respect to its second variable - sometimes, mere convexity is enough - the convergence to steady states is proved. This study is applied to understand the dynamics of a front whose propagation is given by a law of the form

Vn=R(X)

where R is a periodic function of its variables, and which is used to describe some combustion fronts in solid media. An application to the `hump' effect in solid propellant combustion will be given.

utH(x,Du)=0

with periodic conditions in x or in a bounded domain with Dirichlet conditions. When H is strictly convex with respect to its second variable - sometimes, mere convexity is enough - the convergence to steady states is proved. This study is applied to understand the dynamics of a front whose propagation is given by a law of the form

Vn=R(X)

where R is a periodic function of its variables, and which is used to describe some combustion fronts in solid media. An application to the `hump' effect in solid propellant combustion will be given.