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Ionkin, N.I. (1977) Solution of a Boundary-Value Problem in Heat Conduction with a Non-Classical Boundary Condition. Differential Equations, 13, 204-211.

has been cited by the following article:

• TITLE: On the Inverse Problem of Dupire’s Equation with Nonlocal Boundary and Integral Conditions

  AUTHORS: Coskun Guler, Volkan Oban

  KEYWORDS: Mathematical Finance, Dupire’s Formula, Dupire’s Equation, Local Volatility, Diffusion Equation, Inverse Problem, Well-Posedness

  JOURNAL NAME: Journal of Mathematical Finance, Vol.7 No.4, November 28, 2017

  ABSTRACT: In this study, Inverse Problem for Dupire’s Equation with nonlocal boundary and integral conditions is studied. Then, by means of the some transformation, this equation is converted to diffusion equation. The conditions for the existence and uniqueness of a classical solution of the problem under consideration are established and continuous dependence of (p, v) on the data is shown. It is emphasized that this problem is well-posed.