PROBABILISTIC REPRESENTATIONS AND NUMERICAL ALGORITHMS FOR CLASSICAL AND VISCOSITY SOLUTIONS OF THE CAUCHY PROBLEM FOR QUASILINEAR PARABOLIC SYSTEMS

Ya. I. Belopolskaya; E. I. Nemchenko

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PROBABILISTIC REPRESENTATIONS AND NUMERICAL ALGORITHMS FOR CLASSICAL AND VISCOSITY SOLUTIONS OF THE CAUCHY PROBLEM FOR QUASILINEAR PARABOLIC SYSTEMS

机译：拟线性抛物型方程组Cauchy问题的古典与粘性解的概率表示与数值算法。

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We propose two approaches which allow us to construct probabilistic representations of classical and viscosity solutions of the Cauchy problem for a system of quasilinear parabolic equations. Based on these representations, we develop two numerical algorithms to construct the required solution. The system under consideration arises as a mathematical model of parabolic conservation laws. Bibliography: 14 titles.

机译：我们提出了两种方法，它们使我们能够构造拟线性抛物方程组的柯西问题的经典和粘性解的概率表示。基于这些表示，我们开发了两种数值算法来构造所需的解决方案。所考虑的系统是抛物线守恒律的数学模型。参考书目：14种。

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《Journal of Mathematical Sciences》 |2017年第5期|733-750|共18页
作者
Ya. I. Belopolskaya; E. I. Nemchenko;
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St.Petersburg State University for Architecture and Civil Engineering, St.Petersburg, Russia;

St.Petersburg State University for Architecture and Civil Engineering, St.Petersburg, Russia;

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专利

1. PROBABILISTIC APPROACH TO VISCOSITY SOLUTIONS OF THE CAUCHY PROBLEM FOR SYSTEMS OF FULLY NONLINEAR PARABOLIC EQUATIONS [J] . Ya. I. Belopolskaya, W. A. Woyczynski Journal of Mathematical Sciences . 2013,第6期

机译：完全非线性抛物型方程组Cauchy问题粘性解的概率方法。
2. Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function [J] . Michael V.Klibanov, Nikolaj A.Koshev, JingzhiLi, Journal of inverse and ill-posed problems . 2016,第6期

机译：使用铭刻力量函数的Quasilinear抛物线方程的不含陶池问题的数值解
3. Global existence of classical solutions to the Cauchy problem for a kind of quasilinear hyperbolic systems in divergence form [J] . Guan Y. Journal of Mathematical Analysis and Applications . 2009,第2期

机译：一类散度形式的拟线性双曲系统的柯西问题经典解的整体存在
4. Probabilistic Algorithms for Numerical Construction of Classical Solutions to the Cauchy Problem for Nonlinear Parabolic Systems [C] . Yana Belopolskaya, Anastasija Stepanova International Conference on Analytical and Computational Methods in Probability Theory . 2018

机译：非线性抛物系统Cauchy问题古典解法数值构建的概率算法
5. On the large time behavior of solutions for some degenerate quasilinear parabolic systems [D] . 仙葉, 隆 1992

机译：一类退化的拟线性抛物方程组解的大时间行为
6. New Integral Representations for Solutions of Cauchys Problem for Abstract Parabolic Equations [O] . J. A. Donaldson 1971

机译：抽象抛物方程的柯西问题解的新积分表示
7. Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function [O] . Klibanov, Michael V., Koshev, Nikolaj A., Li, Jingzhi, 2016

机译：拟线性Cauchy问题的数值解使用卡尔曼加权函数的抛物线方程
8. The Numerical Solution of a Quasilinear Parabolic Equation Arising in Polymer Rheology [R] . Markowich, P., Renardy, M. 1981

机译：聚合物流变学中拟线性抛物方程的数值解

PROBABILISTIC REPRESENTATIONS AND NUMERICAL ALGORITHMS FOR CLASSICAL AND VISCOSITY SOLUTIONS OF THE CAUCHY PROBLEM FOR QUASILINEAR PARABOLIC SYSTEMS

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