# 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

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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.

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