Mathematical Sciences: Asymptotic Analysis of Singular Bifurcation, Limit Point Instabilities and Free Boundary Problems and Applications

该研究程序考虑了与奇异分叉方程、极限点不稳定性和自由边界问题有关的一系列数学问题。它们包括随时间变化的参数的影响、稳态分叉和控制缓慢变化的Hopf分叉、通过临界点的缓慢通过、从同宿轨道到周期解的转变等。这些研究结果将直接应用于激光问题和聚合物器件。尤其是胶囊的药物释放速度。

This research program considers a series of mathematical problems connected with singular bifurcation equations, limit point instabilities and free boundary problems. They include effects of time- dependent parameters, steady bifurcation and Hopf bifurcation with a slowly varying control, slow passage through a critical point, transition to periodic solutions from a homoclinic orbit, etc. The research results will have direct applications to laser problems and polymer devices, especially in the rate of drug release from capsules.