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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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
- Boundary Condition
- Heat Transfer
- Generalize Solution
- Elliptic Equation