scholarly journals Higher Order Strong Approximations of Semilinear Stochastic Wave Equation with Additive Space-time White Noise

2014 ◽  
Vol 36 (6) ◽  
pp. A2611-A2632 ◽  
Author(s):  
Xiaojie Wang ◽  
Siqing Gan ◽  
Jingtian Tang
Keyword(s):  
Wave Equation ◽  
White Noise ◽  
Higher Order ◽  
Space Time ◽  
Strong Approximations ◽  
Stochastic Wave Equation

Spatial variation for the solution to the stochastic linear wave equation driven by additive space-time white noise

2018 ◽  
Vol 18 (05) ◽  
pp. 1850036 ◽  
Author(s):  
M. Khalil ◽  
C. A. Tudor ◽  
M. Zili
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
White Noise ◽  
Space Time ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Stochastic Wave Equation ◽  
Quadratic Variations

We study the asymptotic behavior of the spatial quadratic variation for the solution to the stochastic wave equation driven by additive space-time white noise. We prove that the sequence of its renormalized quadratic variations satisfies a central limit theorem (CLT for short). We obtain the rate of convergence for this CLT via the Stein–Malliavin calculus and we also discuss some consequences.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

A space-time BIE method for wave equation problems: the (two-dimensional) Neumann case

2013 ◽  
Vol 34 (1) ◽  
pp. 390-434 ◽  
Author(s):  
S. Falletta ◽  
G. Monegato ◽  
L. Scuderi
Keyword(s):  
Wave Equation ◽  
Space Time ◽  
Two Dimensional

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

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