Study on stochastic partial differential equations with singular coefficients

从界面模型的角度研究了二维Young图运动的非平衡涨落极限。极限用一类随机偏微分方程来描述。此外，还研究了考虑时空随机涨落效应的描述界面生长的方程的平衡解、含分数次微分算子的随机偏微分方程解、调和映射热流中的爆破问题、各向异性Allen-Cahn方程的奇异极限以及界面位置的精确估计。

We have studied the nonequilibrium fluctuation limit for the motion of two dimensional Young diagrams from the aspect of interface model. The limit is described by a certain stochastic partial differential equation. Moreover, the equilibrium solution of the equation which describes the growth of interfaces in consideration of the random fluctuation effect in space and time, the stochastic entropic solution of the stochastic partial differential equation with fractional differential operators, blow-up problem in a harmonic map heat flow, the singular limit of anisotropic Allen-Cahn equations and precise estimates on the position of the interfaces are studied.