Singularity Formation in Nonlinear Evolution Equations Conference, Iowa State University, June 8-9, 2002, Ames, Iowa

Iowa State University, Ames IA

Investigators

Abstract

NSF Award Abstract - DMS-0130702 Mathematical Sciences: Singularity Formation in Nonlinear Evolution Equations Abstract 0130702 Sacks This award supports participants in the conference on Singularity Formation in Nonlinear Evolution Equations held at Iowa State University on June 8-9, 2002. The conference emphasizes recent progress in the theory of singularity formation in nonlinear partial differential equations. The focus is mainly on three topics: singular solutions of systems of partial differential equations, critical exponent phenomena in nonlinear parabolic and hyperbolic equations, and effects of damping and convection. An issue of fundamental importance in the mathematical theory of evolution equations is that of singularity formation. Analysis of this phenomenon can be essential for understanding the physical processes being modeled. One might very roughly divide the subject into three categories: regularity theory (proofs that singularities do not occur), propagation and interaction of singularities results (proofs that singularities persist in some respect) and theory of singularity formation (proofs that singularities must occur, and behavior of solutions near singular points). It is this last topic which is the main theme of the proposed conference, which will provide an excellent opportunity for communication and collaboration among faculty and between senior and junior investigators.