带障碍和Neumann问题的拟线性抛物型偏微分方程的概率方法

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI:10.1051/ps/2019023

Lishun Xiao, Shengjun Fan, D. Tian

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引用次数: 1

摘要

本文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的黏度解。带反射的完全耦合正反向随机微分方程的自适应解的存在唯一性是一个重要的问题。与已有的研究结果相比，我们的结果中偏微分方程解的空间变量存在于一个没有凸性约束的区域，偏微分方程的二阶系数依赖于解的梯度，且系数的要求条件较弱。

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A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems

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.

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.