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<p>Consider the <i>inverse design</i> problem for a scalar conservation law, i.e., the problem of finding initial data evolving into a given profile at a given time. The solution we present below takes into account <i>localizations</i> both in the final interval where the profile is assigned and in the initial interval where the datum is sought, as well as additional <i>a priori</i> <i>constraints</i> on the datum’s range provided by the model. These results are motivated and can be applied to data assimilation procedures in traffic modeling and accidents localization.</p>

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Localized inverse design in conservation laws and Hamilton-Jacobi equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月15日

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  • Rinaldo M. Colombo,
  • Vincent Perrollaz

摘要

Consider the inverse design problem for a scalar conservation law, i.e., the problem of finding initial data evolving into a given profile at a given time. The solution we present below takes into account localizations both in the final interval where the profile is assigned and in the initial interval where the datum is sought, as well as additional a priori constraints on the datum’s range provided by the model. These results are motivated and can be applied to data assimilation procedures in traffic modeling and accidents localization.