Study of singularities arising in nonlinear partial differential differential equations and asymptotic methods

(1)爆破解的动力学性质非线性热方程的爆破解在爆破时间之后，在一定的弱意义上可以连续。Matano从动力系统的角度研究了这类解的动力学。在一类涉及小参数（如ε）的扩散方程中，当ε→0时，其解会形成尖锐的过渡层或界面。Funaki考虑了方程包含随机偏差项的情况。Yanagida研究了非线性热方程中的爆破现象，并推广了Fujita等人的经典结果。(4)竞争系统中的界面运动Mimura研究了三种竞争扩散系统的奇异极限中界面的行为。Matano推广了已有的关于对称性下保序动力系统的理论。然后，他将一般理论应用于行波的稳定性分析和其他问题。

(1) Dynamics of blow-up solutions Some blow-up solutions of a nonlinear heat equation can be continued beyond the blow-up time in a certain weak sense. Matano studied the dynamics of such solutions from the point of view of dynamical systems.(2) Motion of interfaces with random deviation In a class of diffusion equations involving a small parameter, say ε, solutions develop sharp transition layers, or interfaces, as ε→0. Funaki considered the case where the equation involves a random deviation term.(3) Estimate of blow-up time in a nonlinear heat equation Yanagida sutdied blow-up phenomena in a nonlinear heat equation and extended the classical results of Fujita and others.(4) Motion of interface in competition systems Mimura studied the behavior of interfaces that arise in the singular limit of a three-species competition-diffusion system.(5) Order-preserving systems in the presence of symmetry Matano extended the existing theory on order-preserving dynamical systems in the presence of symmetry. He then applied the general theory to the stability analysis of traveling waves and other problems.