An inverse problem for a semilinear parabolic equation
An inverse problem for a semilinear parabolic equation
复制标题
DOI：
10.1088/0266-5611/10/5/009
复制
发表时间：
1994-10
期刊：
影响因子：
2.1
通讯作者：
M. Choulli
中科院分区：
文献类型：
--
作者：
M. Choulli
考虑从超定数据中确定函数p，其中函数p出现在方程delta 1u-Deltau-pu +f（u）=0的初边值问题中.在我们的方法的主要思想是将这个反问题转化为一个非标准的非线性方程的求解问题。利用经典的保持器先验估计和Schauder不动点定理，我们找到了这个方程的解.这个结果使我们能够证明反问题解的存在性。反问题的解对非线性项、边界值和超定数据的连续依赖性也得到了证明。线性情况的结果已经由作者发表。
We consider the determination of a function p from overspecified data, where the function p appears in an initial-boundary value problem for the equation delta 1u- Delta u-pu+f(u)=0. The main idea in our approach consists of transforming this inverse problem into the problem of finding a solution to a non-standard non-linear equation. Using the classical Holder a priori estimates and the Schauder fixed-point theorem, we find a solution to this equation. This result then enables us to show the existence of a solution to the inverse problem. The continuous dependence of the solution to the inverse problem on the non-linear term, the boundary-value, and the overdetermined data, is also proved. Results for the linear case have already been published by the author.