Аннотация
We study the Cauchy problem for an almost linear first order differential equation with discontinuous coefficient of the time-derivative. We analyze differential properties of a weak solution to the forward problem and study the inverse problem of finding the discontinuity lines for the time-independent coefficient. For this purpose the trace of a solution to the Cauchy problem is assumed to be given on a plane far from the line in question. We develop an algorithm for solving the inverse problem. Our study can be considered as a fragment of the theory of probing inhomogeneous media by physical signals.
Язык оригинала | английский |
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Страницы (с-по) | 709-726 |
Число страниц | 18 |
Журнал | Journal of Mathematical Sciences (United States) |
Том | 246 |
Номер выпуска | 6 |
DOI | |
Состояние | Опубликовано - 1 мая 2020 |