Existence of a Solution of the Inverse Coefficient Problem for a Quasilinear Hyperbolic Equation

被引：3

作者：

Denisov, A. M. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow 119992, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2019年 / 59卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

quasilinear hyperbolic equation; problem with data on characteristics; inverse problem; existence theorem; nonlinear operator equation;

D O I：

10.1134/S096554251904002X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A problem with data on the characteristics for a quasilinear hyperbolic equation is considered. An inverse problem consisting in determining the unknown coefficient of the equation, depending on its solution, is formulated. As additional information for the inverse problem, the values of the solution of the problem with the data on the characteristics at a fixed value of one of the independent variables are specified. The existence theorem for the inverse problem is proved. The proof is based on deriving a nonlinear operator equation for the unknown coefficient and the proof of its solvability.

引用

页码：550 / 558

页数：9

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