On the uniqueness of solution Cauchy's inverse problem for the equation Δu=au+b

Article type: Research Article

Authors: Bezrodnykh, S.I. | Demidov, A.S.

Affiliations: Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow 119333, Russia and Sternberg Astronomical Institute, MSU, Moscow 119992, Russia. E-mail: sergeyib@pochta.ru | Lomonosov Moscow State University, Moscow 119899, Russia and Moscow Institute of Physics and Technology, Moscow Oblast' 141700, Russia. E-mail: alexandre.demidov@mtu-net.ru

Abstract: The inverse Cauchy problem Δu(x)=au(x)+b≥0  for x∈ω,  and  u=0,   ∂u/∂ν=Φ   on γ is shown as having a unique solution within a wide class of simply connected domains ω⋐R2 with smooth boundary γ. Here a and b are real numbers to be determined, and Φ is a given function which is normalized by the condition ∫γΦ ds=1.

Keywords: inverse Cauchy problem, Grad–Shafranov equation, Vishik–Lyusternik's method, multipole method

DOI: 10.3233/ASY-2011-1047

Journal: Asymptotic Analysis, vol. 74, no. 1-2, pp. 95-121, 2011