Entropy and elliptic equations
Author:
W. A. Day
Journal:
Quart. Appl. Math. 51 (1993), 191-200
MSC:
Primary 35K05; Secondary 35B05, 35J05, 80A10
DOI:
https://doi.org/10.1090/qam/1205946
MathSciNet review:
MR1205946
Full-text PDF Free Access
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Additional Information
J. Fourier, Théorie Analytique de la Chaleur, Paris, 1822
S. Carnot, Réflexions sur la Puissance Motrice du Feu et sur les Machines Propres à Développer cette Puissance, Paris, 1824
- Clifford Ambrose Truesdell III, The tragicomical history of thermodynamics, 1822–1854, Studies in the History of Mathematics and Physical Sciences, vol. 4, Springer-Verlag, New York-Berlin, 1980. MR 584982
- W. A. Day, Parabolic equations and thermodynamics, Quart. Appl. Math. 50 (1992), no. 3, 523–533. MR 1178432, DOI https://doi.org/10.1090/qam/1178432
J. Kestin, ed., The Second Law of Thermodynamics, Benchmark papers on Energy/5, Dowden, Hutchinson, and Ross, Stroudsburg, PA, 1976
- Bernard D. Coleman and Walter Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13 (1963), 167–178. MR 153153, DOI https://doi.org/10.1007/BF01262690
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1977. Grundlehren der Mathematischen Wissenschaften, Vol. 224. MR 0473443
- Carlo Miranda, Partial differential equations of elliptic type, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, Springer-Verlag, New York-Berlin, 1970. Second revised edition. Translated from the Italian by Zane C. Motteler. MR 0284700
J. Fourier, Théorie Analytique de la Chaleur, Paris, 1822
S. Carnot, Réflexions sur la Puissance Motrice du Feu et sur les Machines Propres à Développer cette Puissance, Paris, 1824
C. Truesdell, The Tragicomical History of Thermodynamics 1822–1854, Springer-Verlag, New York, 1980
W. A. Day, Parabolic equations and thermodynamics, Quart. Appl. Math. 50, 523–533 (1992)
J. Kestin, ed., The Second Law of Thermodynamics, Benchmark papers on Energy/5, Dowden, Hutchinson, and Ross, Stroudsburg, PA, 1976
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178 (1963)
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977
C. Miranda, Partial Differential Equations of Elliptic Type, 2nd revised ed., Springer-Verlag, Berlin, 1970
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Article copyright:
© Copyright 1993
American Mathematical Society
