Nonstationary problem of complex heat transfer in a system of semitransparent bodies with boundary-value conditions of diffuse reflection and refraction of radiation

DOI10.1007/s10958-018-3967-xzbMath1462.35391OpenAlexW2886955917MaRDI QIDQ1618291

Andrey A. Amosov

Publication date: 13 November 2018

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3967-x

zbMATH Keywords

stabilityweak solutionexistenceuniquenessa priori estimatesheat transferradiation transfernonstationary problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stability in context of PDEs (35B35) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Positive solutions to PDEs (35B09) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for mixed-type systems of PDEs (35M33) Diffusive and convective heat and mass transfer, heat flow (80A19) Radiative heat transfer (80A21)

Related Items (13)

Initial-boundary value problem for the equations of radiative heat transfer with Fresnel conjugation conditions ⋮ On the global solvability of a boundary value problem for the equations of a viscous heat-conducting gas under the radiative transfer conditions ⋮ Inhomogeneous problem for quasi-stationary equations of complex heat transfer with reflection and refraction conditions ⋮ Optimal control of quasi-stationary equations of complex heat transfer with reflection and refraction conditions ⋮ Nonstationary radiative–conductive heat transfer problem in an absolutely black body with semitransparent inclusions ⋮ Problem of radiation heat exchange with boundary conditions of the Cauchy type ⋮ Inhomogeneous boundary value problem for complex heat transfer equations with Fresnel matching conditions ⋮ Quasi-static diffusion model of complex heat transfer with reflection and refraction conditions ⋮ Stability of stationary solutions of the radiative heat transfer equations ⋮ Unique solvability of a stationary radiative-conductive heat transfer problem in a semitransparent body with absolutely black inclusions ⋮ Stationary problem of radiative heat transfer with Cauchy boundary conditions ⋮ Inverse problem for equations of complex heat transfer ⋮ Nonstationary complex heat transfer problem in a system of grey bodies with semitransparent inclusions

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