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Inhomogeneous boundary value problem for complex heat transfer equations with Fresnel matching conditions. (English. Russian original) Zbl 1459.35176

Differ. Equ. 56, No. 12, 1628-1633 (2020); translation from Differ. Uravn. 56, No. 12, 1660-1665 (2020).
Summary: We consider an inhomogeneous boundary value problem for a system of semilinear elliptic equations modeling radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. The unique solvability of the boundary value problem is proved without requiring the initial data to be small.

MSC:

35J61 Semilinear elliptic equations
35J47 Second-order elliptic systems
35J25 Boundary value problems for second-order elliptic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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