Burgers equation with random boundary conditions

Burgers Equation with Random Boundary Conditions

We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.

Derive boundary conditions for holistic discretisations of Burgers’ equation

I previously used Burgers’ equation to introduce a new method of numerical discretisation of pdes. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models all the processes and their subgrid scale interactions. Here I show how boundaries to the physical domain may be naturally incorporated into the numerical modelling of Burgers’ equation. W...

Numerical analysis of Burgers’ equation with uncertain boundary conditions using the stochastic Galerkin method

Burgers’ equation with stochastic initial and boundary conditions is investigated by a polynomial chaos expansion approach where the solution is represented as a series of stochastic, orthogonal polynomials. The analysis of wellposedness for the stochastic Burgers’ equation follows the pattern of that of the deterministic Burgers’ equation. We use dissipation and spatial derivative operators sa...

-Stable Derivative-Free Error-Corrected Trapezoidal Rule for Burgers' Equation with Inconsistent Initial and Boundary Conditions

PDFs for the Random Forced Burgers Equation

We propose a new approach for the analysis of stationary correlation functions of 1D Burgers equation driven by a random force. We use this to study the asymptotic behavior of the probability distribution of velocity gradients and velocity increments. PACS number 47.27.Gs, 03.40.Gc Statistical properties of solutions of random forced Burgers equation have been a subject of intensive studies rec...