Two results concerning asymptotic behavior of solutions of the Burgers equation with force
Abstract
We consider the Burgers equation with an external force. For the case of the force periodic in space and time we prove the existence of a solution periodic in space and time which is the limit of a wide class of solutions as t → ∞. If the force is the product of a periodic function of x and white noise in time, we prove the existence of an invariant distribution concentrated on the space of spaceperiodic functions which is the limit of a wide class of distributions as t → ∞.
 Publication:

Journal of Statistical Physics
 Pub Date:
 July 1991
 DOI:
 10.1007/BF01057866
 Bibcode:
 1991JSP....64....1S
 Keywords:

 Burgers equation;
 white noise;
 local central limit theorem;
 partition function