The Cauchy problem for the wave equation with Levy noise initial data

Oksendal B; Proske F; Signahl M

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The Cauchy problem for the wave equation with Levy noise initial data

机译：具有Levy噪声初始数据的波动方程的Cauchy问题。

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摘要

In this paper we study the Cauchy problem for the wave equation with spacetime Levy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C-2-solution, which takes an explicit form. Our approach is based on the use of the Hermite transform.

机译：本文研究了随机分布的Kondratiev空间中含时空征费初始数据的波动方程的柯西问题。我们证明此问题具有强大而独特的C-2-解决方案，采用明确的形式。我们的方法基于Hermite变换的使用。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2006年第2期|共22页
作者
Oksendal B; Proske F; Signahl M;
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正文语种 eng
中图分类物理学;
关键词
Cauchy problem; stochastic wave equation; Levy noise initial data; spacetime Levy white noise; Hermite transform; WHITE-NOISE; STABILITY; BOUNDARY; SYSTEMS;

机译：Cauchy问题;随机波动方程;Levy噪声初始数据;时空Levy白噪声;Hermite变换;白噪声;稳定性;边界;系统;

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1. The Cauchy problem for the wave equation with Levy noise initial data [J] . Oksendal B, Proske F, Signahl M Infinite dimensional analysis, quantum probability, and related topics . 2006,第2期

机译：具有Levy噪声初始数据的波动方程的Cauchy问题。
2. On the Cauchy problem for a nonlinear variational wave equation with degenerate initial data [J] . Yanbo Hu, Guodong Wang Nonlinear Analysis: An International Multidisciplinary Journal . 2018,第期

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3. On the dispersionless KadomtsevPetviashvili equation in n+1 dimensions: Exact solutions, the Cauchy problem for small initial data and wave breaking [J] . Manakov S.V., Santini P.M. Journal of physics, A. Mathematical and theoretical . 2011,第40期

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4. Global Well‐Posedness of Cauchy Problem for 1D Generalized Boussinesq Equations at Both Low Initial Energy Level and Critical Initial Energy Level [C] . Jiang Xiaoli, Ding Yunhua, Liu Yacheng, International Conference on Numerical Analysis and Applied Mathematics . 2011

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5. The Euler Equations of an Inviscid Incompressible Fluid Driven by a Levy Noise [D] . Tang, Sisi. 2020

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6. On the initial value problem for the wave equation in Friedmann–Robertson–Walker space–times [O] . Bilal Abbasi, Walter Craig -1

机译：关于Friedmann–Robertson–Walker时空中波动方程的初值问题
7. The Cauchy Problem of Null Form Wave Equation on Td with Random Initial Data [O] . Sijia Zhong 2012

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The Cauchy problem for the wave equation with Levy noise initial data

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