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.

许多物理现象都是用偏微分方程来模拟的，而非线性对于真实的描述是必不可少的。对于不断发展的表面或界面，有趣的行为，如奇点形成强烈联系到所涉及的方程的非线性结构。研究小组的主要课题是：- 几何演化方程（Willmore流和相关的四阶抛物流，Minkowski空间中的最小超曲面，-最小和全纯层积（驯服几乎复环面中的复线，最小轨道和Hamilton-Jacobi方程，-流体中的非线性效应（广义牛顿和电流变流体，具有毛细管自由边界的流体，热弹性和可压缩流体中的物理转变）。共同的目标是在理论和数值分析之间的密切相互作用中，发展求解相关方程的方法。潜在的数学困难往往有一个共同的根源。对这些问题的分析将导致对非线性机制的更好理解，并且要开发的数学工具与未来有关。applications.http://home.mathematik.uni-freiburg.de/fg/Der链接的角度是正确的。