Asymptotical Normality of a Solution of Burgers’ Equation with Random Initial Data

1992 ◽  
Vol 36 (2) ◽  
pp. 217-236 ◽  
Author(s):  
A. V. Bulinskii ◽  
S. A. Molchanov
Keyword(s):  
Initial Data ◽  
Burgers Equation ◽  
Random Initial Data ◽  
Asymptotical Normality

The law of the iterated logarithm for the solution of the Burgers equation with random initial data

1998 ◽  
Vol 64 (6) ◽  
pp. 704-713 ◽  
Author(s):  
Yu. Yu. Bakhtin
Keyword(s):  
Initial Data ◽  
Burgers Equation ◽  
Random Initial Data ◽  
Iterated Logarithm ◽  
The Law

Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data

2012 ◽  
Vol 3 (3) ◽  
pp. 341-358 ◽  
Author(s):  
Alberto Bressan ◽  
Deling Wei
Keyword(s):  
Initial Data ◽  
Differential Games ◽  
Random Initial Data ◽  
Feedback Type ◽  
Stackelberg Solutions

scholarly journals Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data

2019 ◽  
Vol 7 (3) ◽  
pp. 806-837
Author(s):  
James M. Scott ◽  
M. Paul Laiu ◽  
Cory D. Hauck
Keyword(s):  
Initial Data ◽  
Balance Laws ◽  
Random Initial Data ◽  
Hyperbolic Balance Laws

scholarly journals Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ting Zhang ◽  
Chun Shen
Keyword(s):  
Shock Wave ◽  
Initial Data ◽  
Riemann Problem ◽  
Wave Solution ◽  
Burgers Equation ◽  
Explicit Computation ◽  
Convective Term ◽  
Regularization Technique ◽  
Shock Wave Solution

The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.

scholarly journals SCALING LIMITS FOR TIME-FRACTIONAL DIFFUSION-WAVE SYSTEMS WITH RANDOM INITIAL DATA

2010 ◽  
Vol 10 (01) ◽  
pp. 1-35 ◽  
Author(s):  
GI-REN LIU ◽  
NARN-RUEIH SHIEH
Keyword(s):  
Initial Data ◽  
Initial Conditions ◽  
Scaling Limit ◽  
Reaction Diffusion ◽  
Equation System ◽  
Random Initial Data ◽  
Diffusion Type ◽  
Diffusion Wave ◽  
Decoupling Method ◽  
Time Space

Let w (x, t) := (u, v)(x, t), x ∈ ℝ3, t > 0, be the ℝ2-valued spatial-temporal random field w = (u, v) arising from a certain two-equation system of time-fractional linear partial differential equations of reaction-diffusion-wave type, with given random initial data u(x,0), ut(x,0), and v(x,0), vt(x,0). We discuss the scaling limit, under proper homogenization and renormalization, of w(x,t), subject to suitable assumptions on the random initial conditions. Since the component fields u,v depend on the interactions present within the system, we employ a certain stochastic decoupling method to tackle this component dependence. The work shows, in particular, the various non-Gaussian scenarios proposed in [4, 13, 17] and the references therein, for the single diffusion type equations, in classical or in fractional time/space derivatives, can be studied for the two-equation system, in a significant way.

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