Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients

D. S. Anikonov, D. S. Konovalova

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)709-726
Number of pages18
JournalJournal of Mathematical Sciences (United States)
Volume246
Issue number6
DOIs
Publication statusPublished - 1 May 2020

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