Équation de Burgers avec conditions initiales à accroissements indépendants et homogènes
| Autor: | Jean Duchon, Laurent Carraro |
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| Rok vydání: | 1998 |
| Předmět: | |
| Zdroj: | Annales de l'Institut Henri Poincare (C) Non Linear Analysis. 15(4):431-458 |
| ISSN: | 0294-1449 |
| DOI: | 10.1016/s0294-1449(98)80030-9 |
| Popis: | We study here solutions of inviscid Burgers equation with a stochastic initial value with homogeneous and independent increments without positive jumps. We define the notion of intrinsic statistical solution of this evolution equation and show that a family (X (t); t ≥ 0) of homogeneous Levy processes is an intrinsic statistical solution of Burgers equation if and only if the exponent functions ψ (t, w) satisfy the differential equation: ∂tψ = i ψ ∂w ψ. The existence of such solutions follows then from the examination of that last equation. The case of a brownian initial condition is made explicit. |
| Databáze: | OpenAIRE |
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