ANALYSIS AND NUMERICAL SOLVABILITY OF BACKWARD-FORWARD CONSERVATION LAWS.

In this paper, we study the problem of initial data identification for weak-entropy solutions of 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 time-irreversibility of the Burgers equation, some target functions are unattainable from solutions of this equation, making the identification problem under consideration ill-posed. To get around this issue, we introduce a nonsmooth optimization problem, which consists in minimizing the difference between the predictions of the Burgers equation and the observations of the system at a final time in L² (ℝ) norm. Here, we characterize the set of minimizers of the aforementioned nonsmooth optimization problem. One of the minimizers is the backward entropy solution, constructed using a backward-forward method. Some simulations are given using a wave-front tracking algorithm. [ABSTRACT FROM AUTHOR]