Mathematical Sciences: Analysis, Control, Dynamics and Visualization of Distributed Parameter Systems Containing Nonlinearities

小行星9610076 主要研究者将学习二阶偏微分 椭圆型、抛物型和双曲型方程 的非线性。目标是：（a）探索空间-时间 一维波动方程的混沌振动现象 非线性边界条件;（B）边界元素的使用， 拟单调迭代技术来分析和计算控制 具有点观测的半线性椭圆-抛物耦合方程组 （c）国家和控制的可视化 通过改变所涉及的几何形状， 以了解控制效果。 两位研究人员将开发有效和创新的理论， 以及研究所涉及的非线性问题的数值工具。这 研究有望通过可视化增强对 复杂的非线性现象和模式的形成在许多领域， 机械振动，声学，数学生物学，恒化器和 化学反应堆和生态学。这反过来又将进一步帮助 为非线性科学发展新的数学技术。

9610076 Chen The principal investigators will study second order partial differential equations of elliptic, parabolic and hyperbolic types containing certain types of nonlinearities. The objectives are: (a) The exploration of spatio-temporal chaotic vibration phenomena for the one dimensional wave equation with nonlinear boundary conditions; (b) The use of boundary elements and quasimonotone iteration techniques to analyze and compute controlled coupled semilinear elliptic and parabolic systems with point observations and inequality control constraints; (c) Visualization of state and control on annular and dumbbell-shaped domains by varying the geometries involved in order to understand the control effects. The two investigators will develop effective and innovative theoretical as well as numerical tools to study the nonlinear problems involved. This research promises to enhance, through visualization, the understanding of complex nonlinear phenomena and pattern formation in many fields such as mechanical vibration, acoustics, mathematical biology, chemostat and chemical reactors, and ecology. This in turn will further aid in the development of new mathematical techniques for nonlinear sciences.