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Title: The optimization of the stationary heat equation with a variable right-hand side (English)
Author: Matyska, Ctirad
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 31
Issue: 2
Year: 1986
Pages: 97-108
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: Solving the stationary heat equation we optimize the temperature on part of the boundary of the domain under investigation. First the Poisson equation is solved; both the Neumann condition on part of the boundary and the Newton condition on the rest are prescribed, the distribution of the heat sources being variable. In the second case, the heat equation also contains a convective term, the distribution of heat sources is specified and the Neumann condition is variable on part of the boundary. (English)
Keyword: distribution of heat sources
Keyword: Neumann boundary condition
Keyword: Newton boundary condition
Keyword: stationary heat equation
Keyword: Poisson equation
Keyword: boundary value problem
MSC: 35J25
MSC: 49A22
MSC: 49K20
MSC: 80A20
idZBL: Zbl 0629.35034
idMR: MR0837471
DOI: 10.21136/AM.1986.104190
Date available: 2008-05-20T18:29:33Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] D. J. Andrews: Numerical Simulation of Sea-floor Spreading.J. Geoph. Res. 77 (1972), 6470-6481. 10.1029/JB077i032p06470
Reference: [2] S. Fučík A. Kufner: Nonlinear Differential Equations.Elsevier, Amsterdam, 1980. MR 0558764
Reference: [3] S. Fučík J. Nečas V. Souček: Einführung in die Variationsrechnung.Teubner, Leipzig 1977. MR 0487654
Reference: [4] Y. Ida: Thermal Circulation of Partial Melt and Volcanism behind Trenches.Oceanol. Acta, 1981. Proc. 26th Intern. Geolog. Congress, Geology of Continental Margins Symposium, Paris 1980, July 7-17, p 241-244.
Reference: [5] A. Kufner O. John S. Fučík: Function Spaces.Academia, Praha 1977. MR 0482102
Reference: [6] X. LePichon J. Francheteau J. Bonnin: Plate Tectonics.Elsevier, Amsterdam etc. 1973.
Reference: [7] A. Marocco O. Pironneau: Optimum Design with Lagrangian Finite Elements: Design of an Electromagnet.Соmр. Meth. in Appl. Math. 15 (1978), 277-308.
Reference: [8] C. Matyska: The thermal Field of the Lithosphere in the Region of Mid-ocean Ridges Modelled on the Basis of Known Surface Temperature and Heat Flows.Studia geoph. et geodet. 28 (1984), 407-417.
Reference: [9] D. P. McKenzie J. M. Roberts N. O. Weiss: Convection in the Earth's Mantle: towards a Numerical Simulation.J. Fluid Mech. 62 (1974), part 3, 465-538.
Reference: [10] S. Mizohata: Теория уравнений с частными производными.Mir, Moskva 1977 (translated from Japanese).
Reference: [11] D. R. Moore N. O. Weiss: Two-dimensional Rayleigh-Bénard Convection.J. Fluid. Mech. 58 (1973), part 2, 289-312.
Reference: [12] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584
Reference: [13] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elastico-Plastic Bodies: An Introduction.Elsevier, Amsterdam etc. 1981. MR 0600655
Reference: [14] P. Olson K. M. Corcos: A Boundary Layer Model for Mantle Convection with Surface Plates.Geoph. J. R. Astr. Soc. 62 (1980), 195-219. 10.1111/j.1365-246X.1980.tb04851.x
Reference: [15] K. Rektorys: Variational Methods.Reidel C., Dordrecht-Boston 1977. MR 0487653
Reference: [16] G. Schubert C. Froidevaux D. A. Yuen: Oceanic Lithosphere and Asthenosphere: Thermal and Mechanical Structure.J. Geoph. Res. 81 (1976), 3525-3540. 10.1029/JB081i020p03525
Reference: [17] J. G. Sclater J. Francheteau: The Implications of Terrestrial Heat Flow Observations on Current Tectonic and Geochemical Models of the Crust and Upper Mantle of the Earth.Geoph. J. R. Astr. Soc. 20 (1970), 509-542. 10.1111/j.1365-246X.1970.tb06089.x
Reference: [18] L. D. Turcotte E. R. Oxburgh: Mantle Convection and the New Global Tectonics.Ann. Rev. Fluid. Mech. 4 (1972), 33-68. 10.1146/annurev.fl.04.010172.000341


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