Paul C. Fife

Patterns formation in gradient systems

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

July 11 2000