Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary \(p\)-summable right-hand side.

DOI10.1007/s10492-010-0005-9zbMath1224.35057OpenAlexW2089592882MaRDI QIDQ622848

Pierre-Étienne Druet

Publication date: 11 February 2011

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/37841

zbMATH Keywords

nonlinear parabolic equationnonlocal boundary conditionradiative heat transferright-hand side in \(L^1\)

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat equation (35K05) Initial value problems for second-order parabolic equations (35K15) Weak solutions to PDEs (35D30)

Related Items (8)

Nonstationary problem of complex heat transfer in a system of semitransparent bodies with boundary-value conditions of diffuse reflection and refraction of radiation ⋮ Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals ⋮ Noncompactness of integral operators modeling diffuse-gray radiation in polyhedral and transient settings ⋮ Nonstationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency ⋮ Nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields ⋮ Unique solvability of a stationary radiative-conductive heat transfer problem in a semitransparent body with absolutely black inclusions ⋮ Optimal control of semiconductor melts by traveling magnetic fields ⋮ Radiative heating of a glass plate

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