Nonuniqueness of Unbounded Solutions of the Cauchy Problem for Scalar Conservation Lawsстатья
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Дата последнего поиска статьи во внешних источниках: 4 мая 2020 г.
Аннотация:This article is aimed at studying the Cauchy problem for a first-order quasi-linear equationwith a flow function of power type and unbounded initial data of power or exponential type. It is knownthat the Cauchy problem in the class of locally bounded functions may have several solutions. We describeall entropy solutions of this problem, which can be represented in a special form. It is shown that afterthe first discontinuity line (shock wave), these solutions eventually exhibit the same behavior, and theirnonuniqueness actually amounts to the choice of the first shock wave.