On an inverse problem of determining a support of a source term in an elliptic equation
On an inverse problem of determining a support of a source term in an elliptic equation
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关于确定椭圆方程源项支持度的反问题
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Masahiro Yamamoto
中科院分区：
文献类型：
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作者：
Sungwhan Kim;Masahiro Yamamoto
在本文中，我们将给出一个更简单的证明，证明我们已经在预印本UTMS 2001-30（东京大学数学科学研究生院，2001）中讨论过的以下反问题的唯一性：我们考虑一个确定椭圆方程− <$u（x）+ q（x）× D（x）u（x）= 0，x ∈ Ω和u（x）= f（x），x ∈ <$Ω中源项支撑D的反问题。这里q是给定的正函数，χD是子域D的特征函数，使得D <$Ω。本文证明了该反问题在多边形D的凸包内的全局唯一性。
In this paper, we will give a simpler proof for the uniqueness in the following inverse problem which we have already discussed in Preprint UTMS 2001-30 (Graduate School of Mathematical Sciences, The University of Tokyo, 2001):We consider an inverse problem of identifying the support D of a source term in an elliptic equation −∆u(x) + q(x)χD(x)u(x) = 0, x ∈ Ω and u(x) = f(x), x ∈ ∂Ω. Here q is a given positive function and χD is the characteristic function of a subdomain D such that D ⊂ Ω. In this paper, we prove the global uniqueness in this inverse problem within convex hulls of polygons D’s.