Blow-up phenomena in semilinear elliptic partial differential equations

本计画将探讨半线性椭圆型偏微分方程的重要问题。它将决定的存在，多重性，对称性破缺，浓度现象， 半线性偏微分方程的解半线性方程解的渐近性态对微分方程应用于简单力学系统的领域有着巨大的影响潜力，也可以应用于各种自然现象，如吊桥、星系和数学生物学问题。

This project will address important questions in semilinear elliptic partial differential equations. It will determine the existence, multiplicity, breaking of symmetry, and concentration phenomena of solutions of semilinear partial differential equations. The asymptotic behaviour of solutions in semilinear equations has enormous potential to impact on fields in which differential equations can be applied to simple mechanical systems, and built and diverse natural phenomena such as suspension bridges, galaxies and mathematical biology problems.