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A positive solution of an elliptic equation with nonlinear integral boundary condition of the radiation type

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Abstract

The problem for an elliptic equation with a nonlinear integral boundary condition describing, in particular, a stationary radiative heat transfer according to the Stefan-Boltzmann law in a system of blackbodies is considered. Theorems about the existence, uniqueness, and stability of the positive generalized solution are established.

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Literature cited

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Additional information

Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 117–128, July, 1977.

The author thanks N. S. Bakhvalov for suggesting the problem and guiding the work.

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Amosov, A.A. A positive solution of an elliptic equation with nonlinear integral boundary condition of the radiation type. Mathematical Notes of the Academy of Sciences of the USSR 22, 555–561 (1977). https://doi.org/10.1007/BF01147699

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Keywords

  • Radiation
  • Boundary Condition
  • Heat Transfer
  • Generalize Solution
  • Elliptic Equation