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Title: The inverse problem of recovering the source in a parabolic equation under a condition of nonlocal observation

We study the inverse problem for a parabolic equation of recovering the source, that is, the right-hand side F(x,t)=h(x,t)f(x), where the function f(x) is unknown. To find f(x), along with the initial and boundary conditions, we also introduce an additional condition of nonlocal observation of the form ∫{sub 0}{sup T}u(x,t) dμ(t)=χ(x). We prove the Fredholm property for the problem stated in this way, and obtain sufficient conditions for the existence and uniqueness of a solution. These conditions are of the form of readily verifiable inequalities and put no restrictions on the value of T>0 or the diameter of the domain Ω under consideration. The proof uses a priori estimates and the qualitative properties of solutions of initial-boundary value problems for parabolic equations. Bibliography: 40 titles.
Authors:
 [1]
  1. National Research Nuclear University 'Moscow Engineering Physics Institute', Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22365951
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY CONDITIONS; BOUNDARY-VALUE PROBLEMS; CALCULATION METHODS; FUNCTIONS; INVERSE SCATTERING PROBLEM; MATHEMATICAL SOLUTIONS