一个非线性随机偏微分方程解的存在惟一性

Existence and uniqueness of solution for a nonlinear stochastic differential equation

对一个随机偏微分方程,首先利用不动点定理给出局部解的存在惟一性,并利用解对初值的连续依赖,给出整体解的存在惟一性。

For a nonlinear stochastic differential equation, the existence and uniqueness of the local solution is given based on the fixed point theorem. With the continuous dependency of the solution on initial value, the existence and uniqueness of global solution is proved.