Nonlinear partial differential equations: Theoretical and numerical analysis

非线性偏微分方程：理论和数值分析

• 批准号: 5363386
• 负责人: Professor Dr. Ernst Kuwert
• 金额: --
• 依托单位: Abteilung für Reine Mathematik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2002
• 资助国家: 德国
• 起止时间: 2001-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5363386?language=en
• 关键词: Nonlinear; partial; differential; equations; Theoretical

Many physical phenomena are modelled by partial differential equations, and nonlinearities are essential for a realistic description. For evolving surfaces or interfaces, interesting behaviour like singularity formation is strongly linked to the nonlinear structure of the equations involved. The main topics of the research group are: -geometric evolution equations (Willmore flow and related fourth order parabolic flows, minimal hypersurfaces in Minkowski space,-minimal and holomorphic laminations (complex lines in tame almost comlex tori, minimal orbits and Hamilton-Jacobi equations,-nonlinear effects in fluids (generalized Newtonian and electrorheological fluids, fluids with cappilary free boundaries, physe transitions in thermoelasticity and compressible fluids).The common goal is to develop methods for solving the related equations, in a close interplay between theoretical and numerical analysis. The underlying mathematical difficulties often have a common source. The analysis of those problems will lead to an improved understanding of the nonlinear mechanisms, and the mathematical tools to be developed are relevant to future applications.http://home.mathematik.uni-freiburg.de/fg/Der Text der Zusammenfassung ist der oben angegebenen Seite zu entnehmen. Die Angabe des Links ist ausreichend.

许多物理现象是由部分微分方程建模的，非线性对于现实描述至关重要。对于不断发展的表面或接口，诸如奇异性形成之类的有趣行为与所涉及方程的非线性结构密切相关。 The main topics of the research group are: -geometric evolution equations (Willmore flow and related fourth order parabolic flows, minimal hypersurfaces in Minkowski space,-minimal and holomorphic laminations (complex lines in tame almost comlex tori, minimal orbits and Hamilton-Jacobi equations,-nonlinear effects in fluids (generalized Newtonian and electrorheological流体，具有钙的自由边界的液体，热弹性中的Physe转变和可压缩的流体）。共同的目标是开发解决相关方程的方法，在理论和数学上的数字分析之间的近距离相互作用通常会导致对这些问题的相关性。对未来的应用程序。