Global and blowup solutions for quasilinear parabolic equations and their numerical computations

拟线性抛物型方程的全局解和爆炸解及其数值计算

• 批准号: 251200-2008
• 负责人: Chen, Shaohua(George)
• 金额: $ 0.87万
• 依托单位: Cape Breton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503710
• 关键词: Global; blowup; solutions; quasilinear; parabolic

Quasilinear degenerate parabolic equations have many applications in Physics, Chemistry, Biology and image processing. These equations involve a degenerate or singular diffusion term and some kinds of blowup properties which create many challenging problems in global, blowup and numerical solutions. The objectives of this research program involve using a new functional method and moving mesh methods to investigate the properties of global and blowup solutions both theoretically and numerically. The expected results will include the following:

准线性退化抛物线方程在物理，化学，生物学和图像处理中有许多应用。这些方程涉及退化或奇异的扩散项以及某些爆炸特性，这些特性在全球，爆炸和数值解决方案中造成了许多具有挑战性的问题。该研究计划的目标涉及使用新的功能方法和移动网格方法来研究全球和爆炸解决方案的属性，从理论和数值上讲。预期结果将包括以下内容：