A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems
A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems
复制标题
具有障碍物和诺伊曼问题的拟线性抛物线偏微分方程的概率方法
DOI：
10.1051/ps/2019023
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Tian Dejian
中科院分区：
文献类型：
--
作者：
Xiao Lishun;Fan Shengjun;Tian Dejian
本文利用概率方法证明了拟线性抛物型偏微分方程结合Neumann边界条件和代数方程的障碍问题存在唯一粘性解。具有反射项的完全耦合正倒向随机微分方程适应解的存在唯一性是一个关键问题。与已有的结果相比，我们的结果中偏微分方程解的空间变量位于一个无凸约束的区域内，偏微分方程的二阶系数依赖于解的梯度，并且对系数的要求条件较弱.
In this paper, by a probabilistic approach we prove that there exists a unique viscosity solution to obstacle problems of quasilinear parabolic PDEs combined with Neumann boundary conditions and algebra equations. The existence and uniqueness for adapted solutions of fully coupled forward-backward stochastic differential equations with reflections play a crucial role. Compared with existing works, in our result the spatial variable of solutions of PDEs lives in a region without convexity constraints, the second order coefficient of PDEs depends on the gradient of the solution, and the required conditions for the coefficients are weaker.