9 Spikes

Numerical studies of solutions to Equations (16View Equation) – (17View Equation) indicate that for most spatial points, behavior similar to that described by the asymptotic expansions (37View Equation) – (38View Equation) occurs [1110]. However, the studies also indicate that there are exceptional spatial points at which the behavior is different. Due to the appearance of the solutions in the neighborhood of the exceptional points, the corresponding features have been referred to as “spiky features” or “spikes”. Their existence would seem to necessitate an understanding of the “spikes” on an analytical level in order to be able to describe the asymptotics of general T3-Gowdy solutions. An important step in this direction was achieved by demonstrating the existence of a large class of solutions to Equations (16View Equation) – (17View Equation) with spikes [71Jump To The Next Citation Point]. In order to be able to describe these solutions, we need to introduce some transformations taking solutions to solutions.

 9.1 Inversion
 9.2 Gowdy to Ernst transformation
 9.3 False spikes
  9.3.1 True spikes
 9.4 High velocity spikes

  Go to previous page Go up Go to next page