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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