The inverse problem consists of simultaneously determining the pair of functions (e.g., {temperature, source term factor}) {u,f}∈C^{2+α}(Ω\bar )×C^α ([0,l]) such that the Poisson equation −Δu(x,y)=f(x)h(x,y)+g(x,y) holds in Ω, the boundary condition u=μ on ∂Ω is satified and the overposed datum is u(x,0)=χ(x), 0≤x≤l.
Crosta, G. (2005). Mathematical Review: MR2096929 (2005h:35369) Solovʹëv, V. V. Inverse problems of source determination for the Poisson equation on the plane. (Russian). MATHEMATICAL REVIEWS.
Mathematical Review: MR2096929 (2005h:35369) Solovʹëv, V. V. Inverse problems of source determination for the Poisson equation on the plane. (Russian)
CROSTA, GIOVANNI FRANCO FILIPPO
2005
Abstract
The inverse problem consists of simultaneously determining the pair of functions (e.g., {temperature, source term factor}) {u,f}∈C^{2+α}(Ω\bar )×C^α ([0,l]) such that the Poisson equation −Δu(x,y)=f(x)h(x,y)+g(x,y) holds in Ω, the boundary condition u=μ on ∂Ω is satified and the overposed datum is u(x,0)=χ(x), 0≤x≤l.
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