A Local Existence Theorem for a Parabolic Blow-Up Inverse Problem.

In this article, we study an inverse problem for a parabolic equation with blow-up initial and boundaryvaluesinthefollowingform: u −u = f(x)u−b(x,t)up (p>1,0<x<1,0<t<T).The inverse problem is to determine the unknown function f(x) from the blow-up rates and the additional 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.

Recommended citation: Yu Pan, Xuran Meng and Wuqing Ning, "A Local Existence Theorem for a Parabolic Blow-Up Inverse Problem." Pure Mathematics, 2017.
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