Martingale Solution to Stochastic Extended Korteweg-de Vries Equation

Anna Karczewska; Maciej Szczeciński

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Martingale Solution to Stochastic Extended Korteweg-de Vries Equation

机译：随机扩展Korteweg-de Vries方程的解决方案

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The deterministic extended Korteweg-de Vries equation plays an essential role in the description of the creation and propagation of nonlinear waves in many fields. We study a stochastic extended Korteweg-de Vries equation driven by a multiplicative noise in the form of a cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied for all physically relevant initial conditions. The proof of the solution is based on two approximations of the problem considered and the compactness method.

机译：确定性扩展的Korteweg-de Vries方程在描述非线性波在许多领域的产生和传播中起着至关重要的作用。我们研究了由圆柱维纳过程形式的乘性噪声驱动的随机扩展Korteweg-de Vries方程。我们证明了针对所有与物理相关的初始条件研究的方程式的ting解的存在。解决方案的证明是基于所考虑问题和紧致度方法的两个近似值。

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《Advances in Pure Mathematics》 |2018年第12期|共16页
作者
Anna Karczewska; Maciej Szczeciński;
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正文语种
中图分类数学;
关键词
Extended Korteweg-de Vries EquationMartingale SolutionStochastic Fluid Dynamics;

机译：扩展的Korteweg-de Vries方程马丁解决方案随机流体动力学;

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专利

1. Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrodinger and linearized stochastic Korteweg-de Vries equations [J] . Harms Philipp, Mueller Marvin S. ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2019,第1期

机译：随机演化方程和应用于非线性随机波，HJMM，随机施罗德格和线性化随机Korteeg-de Vries方程的弱收敛速率
2. On exact solutions for time-fractional Korteweg-de Vries and Korteweg-de Vries-Burger's equations using homotopy analysis transform method [J] . Chinese Journal of Physics . 2020,第期

机译：关于时间分数kortew-de Vries和Korteeg-de Vries-Burger的精确解决方案，使用同型分析变换方法
3. Numerical Solutions of Korteweg-de Vries and Korteweg-de Vries-Burger's Equations in a Bernstein Polynomial Basis [J] . Ahmed H. M. Mediterranean journal of mathematics . 2019,第4期

机译：在伯尔斯坦多项式基地中的数值解决方案或短路 - DE VRIES和短路-DO-DE VRIES-汉堡方程
4. New exact solutions for Korteweg-de Vries Burgers equation and Korteweg-de Vries equation [C] . 2011 International Conference on Management Science and Industrial Engineering . 2011

机译：Korteweg-de Vries Burgers方程和Korteweg-de Vries方程的新精确解
5. Low Regularity Solutions of Korteweg-de Vries and Chern-Simons-Schrodinger Equations. [D] . Liu, Baoping. 2012

机译：Korteweg-de Vries和Chern-Simons-Schrodinger方程的低正则解。
6. Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations [O] . D. V. Chudnovsky, G. V. Chudnovsky 1999

机译：使用正交多项式和Korteweg-de Vries方程求解脉冲宽度调制问题
7. Martingale Solution to Stochastic Extended Korteweg-de Vries Equation [O] . Anna Karczewska, Maciej Szczeciński 2018

机译：随机扩展的Korteweg - de Vries方程的鞅解

Martingale Solution to Stochastic Extended Korteweg-de Vries Equation

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