一非线性发展方程的反问题

An Inverse Problem for a Nonlinear Evolution Equation

英文关键词:evolution equation  inverse problem  semigroup theory  fixed pointmethod.

中文摘要:

      研究一非线性发展方程的未知源项的反演问题.首先，把所考虑的初边值问题化成一等价非线性发展方程的Cauchy问题；然后，利用半群理论，论证反问题解的存在性和唯一性；最后，利用压缩映射不动点方法，得到反问题的可解性.

英文摘要:

      This paper deals with an inverse problem for the unknown source term in a nonlinear evolution equation. Firstly, the authors change the initial boundary value problem (IBVP) for the equation into a Cauchy problem for a certain nonlinear evolution equation. Secondly, using the semigroup theory, the authors establish the existence and uniqueness of the solution for the inverse problem. Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem for the evolution equation.