Time-invariant surfaces in evolution equations

22 April 2013
A time-invariant level surface is a (codimension one) spatial surface on which, for every fixed time, the solution of an evolution equation equals a constant (depending on the time). A relevant and motivating case is that of the heat equation. The occurrence of one or more time-invariant surfaces forces the solution to have a certain degree of symmetry. In my talk, I shall present a set of results on this theme and sketch the main ideas involved, that intertwine a wide variety of old and new analytical and geometrical techniques.
  • Partial Differential Equations Seminar