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. We fully characterize the set of initial data leading to a given target along forward entropic evolution of Burgers equation. The proof is based on a backward-forward method and generalized backward characteristics. Simulations to sonic boom minimization are given using a wave-front tacking 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 1

Citer

Thibault Liard, Enrique Zuazua. Initial data identification for the one-dimensional Burgers equation. 2020. ⟨hal-03028457v1⟩
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