Stable and metastable patterned solutions of nonlinear evolution equations of gradient type are discussed. Examples include classes of higher order parabolic PDE's and integrodifferential equations. A governing theme is that patterns can arise as a result of a competition between opposing influences such as destabilizing and stabilizing mechanisms. The discussion is within the context of a general framework although in the case of conserved evolutions, most attention is given to the Cahn-Hilliard equation and metastable patterns. The focus is on rigorous results; however some important formal stability and modulational theories are also reviewed.
Paul C. Fife
Dept. of Mathematics
University of Utah
155 So. 1400 East
Salt Lake City
Utah 84112-0090
USA
July 11 2000