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：非线性发展方程中的奇点形成该奖项支持2002年6月8-9日在爱荷华州立大学举行的关于非线性发展方程中奇点形成的会议的与会者。会议强调了非线性偏微分方程奇性形成理论的最新进展。主要集中在三个方面：偏微分方程组的奇异解，非线性抛物型和双曲型方程的临界指数现象，以及阻尼和对流的影响。在发展方程的数学理论中，一个重要的问题是奇性的形成。对这一现象的分析对于理解所模拟的物理过程是必不可少的。人们可以非常粗略地将这个主题分为三类：正则性理论(证明奇点不会发生)，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要主题，它将为教职员工之间以及高级和初级调查人员之间的交流和合作提供一个极好的机会。

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.