dorsal/arxiv
View SchemaConnection between the Burgers equation with an elastic forcing term and a stochastic process
| Authors | Eric Moreau, Olivier Vallée |
|---|---|
| Categories | |
| ArXiv ID | physics/0412136 |
| URL | https://arxiv.org/abs/physics/0412136 |
Abstract
We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-\kappa^{2} x+f(t)$, $\kappa\in\mathbb{R}$. Two methods existing for the case $\kappa=0$ are adapted and generalized using variable and function transformations, valid for all values of space an time. The emergence of a Fokker-Planck equation in the method allows to connect a fluid model, depicted by the Burgers equation, with an Ornstein-Uhlenbeck process.
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"date_modified": "2026-03-02T18:00:53.733000Z",
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"abstract": "We present a complete analytical resolution of the one dimensional Burgers\nequation with the elastic forcing term $-\\kappa^{2} x+f(t)$,\n$\\kappa\\in\\mathbb{R}$. Two methods existing for the case $\\kappa=0$ are adapted\nand generalized using variable and function transformations, valid for all\nvalues of space an time. The emergence of a Fokker-Planck equation in the\nmethod allows to connect a fluid model, depicted by the Burgers equation, with\nan Ornstein-Uhlenbeck process.",
"arxiv_id": "physics/0412136",
"authors": [
"Eric Moreau",
"Olivier Vall\u00e9e"
],
"categories": [
"physics.plasm-ph",
"math-ph",
"math.MP"
],
"title": "Connection between the Burgers equation with an elastic forcing term and a stochastic process",
"url": "https://arxiv.org/abs/physics/0412136"
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