具有未知源的某些非线性伪抛物型方程的反问题(英文)

Inverse Problem for Some Nonlinear Pseudo Parabolic Equations with Unknown Source

考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题． 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Ｃｏｕｃｈ ｙ 问题，然 后，利用半 群理论，论 证发展 方程反问 题解的存 在唯一 性，最后， 利用不 动点方法得到 伪抛物型方程反

This paper deals with an inverse problem for some nonlinear pseudo parabolic equations with their unknown source terms. Firstly, the authors change the initial boundary value problem for pseudo parabolic equations into Cauchy problem of the nonlinear evolution equations. Secondly, by using the semigroup theory, the authors establish the existence and uniqueness of solutions of the inverse problem for the evolution equations. Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem of the inverse problem of the pseudo parabolic equations.