Initial data identification for the one-dimensional Burgers equation - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2020

Initial data identification for the one-dimensional Burgers equation

Résumé

In this paper, we study the problem of identification for the one-dimensional Burgers equation. This problem consists in identifying the set of initial data evolving to a given target at a final time. Due to the property of non-backward uniqueness of Burgers equation, there may exist multiple initial data leading to the same given target. In recent works, a fully characterization of the set of initial data leading to a given target is given using the classical Lax-Hopf formula. In this note, an alternative proof based only on generalized backward characteristics is given. This leads to the hope of investigate systems of conservation laws in one dimension where the classical Lax-Hopf formula doesn't hold anymore. Moreover, numerical illustrations are presented using as a target, a function optimized for minimum pressure rise in the context of sonic-boom minimization problems. All of initial data leading to this given target are constructed using a wave-front tracking algorithm.
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Dates et versions

hal-03028457 , version 1 (27-11-2020)
hal-03028457 , version 2 (16-12-2020)

Identifiants

  • HAL Id : hal-03028457 , version 2

Citer

Thibault Liard, Enrique Zuazua. Initial data identification for the one-dimensional Burgers equation. 2020. ⟨hal-03028457v2⟩
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