一类抛物型爆破反问题的局部存在性定理
A Local Existence Theorem for a Parabolic Blow-Up Inverse Problem
DOI: 10.12677/PM.2017.74034, PDF, HTML, XML, 下载: 1,598  浏览: 4,804  科研立项经费支持
作者: 潘宇, 孟徐然, 宁吴庆*：中国科学技术大学，安徽 合肥
关键词: 非线性抛物方程；爆破；反问题；存在性；δ-线；Nonlinear Parabolic Equation； Blow-Up； Inverse Problem； Existence； δ-Line
摘要: 本文研究如下初边值条件均爆破的抛物型方程的反问题： 。此类反问题是由爆破速率和附加观测数据来确定未知函数f(x) 。为了部分消除爆破数据,我们引入δ-线的概念以增加δ-线上的观测数据，从而可将问题简化为经典的反问题。之后建立相关泛函来证明在给定的闭区域中反问题的局部存在性定理。
Abstract: In this article, we study an inverse problem for a parabolic equation with blow-up initial and boundary values in the following form: . The inverse problem is to determine the unknown function f(x) from the blow-up rates and the addi- tional observation data. In order to partly remove the blow-up data, we introduce the definition of δ-line, which allows us to add the observable data and simplifies the inverse problem into a classical one. Then by establishing related functional, we prove a local existence theorem for the inverse problem in somegiven closed domain.
文章引用：潘宇, 孟徐然, 宁吴庆. 一类抛物型爆破反问题的局部存在性定理[J]. 理论数学, 2017, 7(4): 262-270. https://doi.org/10.12677/PM.2017.74034

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