论文标题
将解决方案渐近分解为带有振荡系数的随机抛物线运算符
Asymptotic decomposition of solutions to random parabolic operators with oscillating coefficients
论文作者
论文摘要
我们认为差异的问题是二阶抛物线运算符，其迅速振荡系数在空间变量和随机静止的ergodic中是周期性的。如[25]中所证明的，在这种情况下，均质操作员是确定性的。我们获得了解决方案的渐近扩展的主要术语，这些术语是确定性函数，并表明解决方案和上述领先术语在某些SPDE的溶液中有适当重新归一化的差异。
We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variable and random stationary ergodic in time. As was proved in [25] and [13] in this case the homogenized operator is deterministic. We obtain the leading terms of the asymptotic expansion of the solution , these terms being deterministic functions, and show that a properly renormalized difference between the solution and the said leading terms converges to a solution of some SPDE.
