Previous |  Up |  Next

Article

Keywords:
radiative heat transfer; nonlinear parabolic equation; nonlocal boundary condition; right-hand side in $L^1$
Summary:

References:
[1] Boccardo, L., Gallouët, T.: Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989), 149-169. MR 1025884
[2] Druet, P.-E.: Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right-hand side in $L^p$ ($p\geq1$). Math. Methods Appl. Sci. 32 (2009), 135-166 Available at http://www.wias-berlin.de/publications/preprints/1240 MR 2478911 | Zbl 1151.35319
[3] Hansen, O.: The Radiosity Equation on Polyhedral Domains. Logos Verlag Berlin (2002). Zbl 1005.65143
[4] Klein, O., Philip, P.: Transient conductive-radiative heat transfer: Discrete existence and uniqueness for a finite volume scheme. Math. Models Methods Appl. Sci. 15 (2005), 227-258. MR 2119998 | Zbl 1070.65075
[5] Klein, O., Philip, P., Sprekels, J.: Modeling and simulation of sublimation growth in SiC bulk single crystals. Interfaces Free Bound. 6 (2004), 295-314. MR 2095334
[6] Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N.: Linear and Quasi-linear Equations of Parabolic Type, Vol. 23. Translations of Mathematical Monographs. AMS Providence (1968).
[7] Laitinen, M., Tiihonen, T.: Conductive-radiative heat transfer in grey materials. Q. Appl. Math. 59 (2001), 737-768. MR 1866555
[8] Lewandowski, R.: Analyse mathématique et océanographie. Masson Paris (1997), French.
[9] Lions, J.-L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod/Gauthier-Villars Paris (1969), French. MR 0259693 | Zbl 0189.40603
[10] Metzger, M.: Existence for a time-dependent heat equation with non-local radiation terms. Math. Methods Appl. Sci. 22 (1999), 1101-1119. MR 1706102 | Zbl 0933.35104
[11] Meyer, C., Philip, P., Tröltzsch, F.: Optimal control of a semilinear PDE with nonlocal radiation interface conditions. SIAM J. Control Optim. 45 (2006), 699-721. MR 2246096
[12] Simon, J.: Compact sets in the space $L^p(0,T;B)$. Ann. Mat. Pura Appl., IV. Ser. 146 (1987), 65-96. MR 0916688
[13] Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Instit. Fourier 15 (1965), 189-258 French. MR 0192177 | Zbl 0151.15401
[14] Tiihonen, T.: A nonlocal problem arising from heat radiation on non-convex surfaces. Eur. J. App. Math. 8 (1997), 403-416. MR 1471600 | Zbl 0889.45013
[15] Tiihonen, T.: Stefan-Boltzmann radiation on nonconvex surfaces. Math. Methods Appl. Sci. 20 (1997), 47-57. MR 1429330 | Zbl 0872.35044
[16] Voigt, A.: Numerical simulation of industrial crystal growth. PhD. Thesis Technische Universität München München (2001). Zbl 1009.82001
Partner of
EuDML logo