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

NSF奖摘要- DMS-0130702数学科学：非线性演化方程中的奇点形成摘要0130702萨克斯该奖项支持2002年6月8日至9日在爱荷华州州立大学举行的非线性演化方程中奇点形成会议的与会者。 会议强调了非线性偏微分方程奇异性形成理论的最新进展。重点是三个主题：奇异解的偏微分方程组，临界指数现象的非线性抛物和双曲方程，阻尼和对流的影响。在发展方程的数学理论的一个基本重要问题是，奇异性的形成。对这种现象的分析对于理解被建模的物理过程是必不可少的。人们可以非常粗略地将这个问题分为三类：正则性理论（证明奇点不发生），奇点结果的传播和相互作用（证明奇点在某些方面持续存在）和奇点形成理论（证明奇点必须发生，以及奇点附近的解的行为）。正是这最后一个主题是拟议会议的主题，这将为教师之间以及高级和初级研究人员之间的沟通和合作提供一个绝佳的机会。

NSF Award Abstract - DMS-0130702Mathematical Sciences: Singularity Formation in Nonlinear Evolution EquationsAbstract0130702 SacksThis 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.