TY - JOUR

T1 - Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients

AU - Anikonov, D. S.

AU - Konovalova, D. S.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85084637698&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-04775-4

DO - 10.1007/s10958-020-04775-4

M3 - Article

AN - SCOPUS:85084637698

VL - 246

SP - 709

EP - 726

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 6

ER -