Time-invariant surfaces in evolution equations.
Rolando Magnanini,
(Dipartamento di Matematica e Informatica "U. Dini", Università di Firenze)
26/09/2013 12:00
A stationary or time-invariant surface for a solution of the heat equation is a surface of co-dimension one on which for each fixed time the solution is a constant (depending on time). The definition can be extended to other evolution equations, linear and nonlinear. In presence of initial-boundary values, the existence of one or more time-invariant surfaces generally induces certain symmetries on the solution and its domain. In my talk I will present old and new results about this problem. The techniques developed to treat it involve the use of balance laws, the study of the short- and large-time behavior of the solution, Liouville-type theorems and the method of moving planes.