An existence theorem for an inverse problem for a semilinear hyperbolic system
An existence theorem for an inverse problem for a semilinear hyperbolic system
复制标题
半线性双曲系统反问题的存在定理
DOI：
10.1007/s10625-005-0001-0
复制
发表时间：
2004
影响因子：
0.6
通讯作者：
A. M. Denisov
中科院分区：
文献类型：
--
作者：
A. M. Denisov
本文考虑一类系数依赖于不同解分量的半线性双曲方程组。我们研究的逆问题的基础上找到的附加信息的解决方案的系数之一。反问题的存在性定理的证明是基于后者减少到一个非线性算子方程，这是一个非线性积分微分方程的未知系数。文[1]用这种方法证明了一个拟线性双曲型方程反问题解的存在性。文献[2-6]等也考虑了拟线性双曲型方程和方程组的反问题。
In the present paper, we consider a semilinear hyperbolic system with coefficients depending on different solution components. We study the inverse problem of finding one of the coefficients on the basis of additional information on the solution. The proof of the existence theorem for the inverse problem is based on the reduction of the latter to a nonlinear operator equation, which is a nonlinear integro-differential equation for the unknown coefficient. This approach was used in [1] to prove the existence of a solution of the inverse problem for a quasilinear hyperbolic equation. Inverse problems for quasilinear hyperbolic equations and systems were also considered in [2–6] and other papers.