### 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

USA

July 11 2000