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

(1)爆破解的动力学一类非线性热方程的爆破解在一定弱意义下可以在爆破时间之后继续存在。马塔诺从动力系统的角度研究了这类解的动力学。(2)具有随机偏差的界面的运动在一类涉及小参数的扩散方程中，例如ε，解发展出尖锐的过渡层或界面，如ε→0。Funaki考虑了方程含有随机偏差项的情形。(3)非线性热方程中爆破时间的估计。Yanagida研究了非线性热方程中的爆破现象，推广了Fujita等人的经典结果。(4)竞争系统中界面的运动研究了三种群竞争扩散系统奇异极限下界面的行为。(5)对称性存在下的保序系统推广了现有的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稳定性分析等问题。

(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.