On the propagation of the bulk of a mass subject to periodic convection and diffusion
Authors:
W. A. Day and G. Saccomandi
Journal:
Quart. Appl. Math. 57 (1999), 561-572
MSC:
Primary 35K15; Secondary 35B40, 35Q99
DOI:
https://doi.org/10.1090/qam/1704423
MathSciNet review:
MR1704423
Full-text PDF Free Access
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Additional Information
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M. E. Taylor, Partial Differential Equations II, Applied Math. Sci. 116, Springer-Verlag, Berlin, 1996
T. Miyazawa, Theory of one-variable Fokker-Planck equation, Physical Review A 39, 1447–1468 (1989)
H. Risken, The Fokker-Planck Equation, Springer-Verlag, Berlin, 1984
C. C. Mei, J.-L. Auriault, and Chiu-on Ng, Some applications of homogenization theory, Advances in Applied Mechanics 32, 278–345 (1996)
G. de Marsily, Quantitative Hydrology, Academic Press, New York, 1986
A. J. Majda, Vorticity, turbulence, and acoustics in fluid flow, SIAM Review 33, 349–388 (1991)
R. Racke, Lectures on Nonlinear Evolution Equations: Initial Value Problems, Vieweg u. Sohn, Braunschweig u. Wiesbaden, 1992
C. Cattaneo, Sulla conduzione del calore, Atti del Seminario Matematico Univ. di Modena 3, 83–101 (1948–49)
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31, 113–126 (1968)
D. D. Joseph and L. Preziosi, Heat waves, Rev. Modern Physics 61, 41–73 (1989)
G. Fichera, Is the Fourier theory of heat propagation paradoxical?, Rend. del Circolo Matematico di Palermo 41, 5–28 (1992)
W. A. Day, On rates of propagation of heat according to Fourier’s theory, Quart. Appl. Math. 55, 127–138 (1997)
W. A. Day, A note on the propagation of temperature disturbances, Quart. Appl. Math. 55, 565–572 (1997)
J. C. Maxwell, Theory of Heat, 2nd edition, Longmans, Green and Co., London, 1872
S. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Yale University Press, New Haven, 1969
R. M. Wilcox and R. Bellman, Truncation and preservation of moment properties for Fokker-Planck moment equations, J. Math. Anal. Appl. 32, 532–542 (1970)
R. Aris, On the dispersion of a solute in a fluid flowing through a tube, Proc. Roy. Soc. London Ser. A 235, 67–77 (1956)
S. D. Watt and A. J. Roberts, The accurate dynamic modelling of contaminant dispersion in channels, SIAM J. Appl. Math. 55, 1016–1038 (1995)
G. Toscani, Kinetic approach to the asymptotic behaviour of the solution to diffusion equations, Rend. di Matematica e Applicazioni Serie VII 16, 329–346 (1996)
J. Flavin and S. Rionero, Qualitative Estimates for Partial Differential Equations, CRC Press, Boca Raton, FL, 1995
S. Steinberg and K. B. Wolf, Symmetry, conserved quantities and moments in diffusive equations, J. Math. Anal. and Applications 80, 36–45 (1981)
E. Pucci and G. Saccomandi, Potential symmetries of Fokker-Planck equations in Modern Group Analysis, N. H. Ibragiminov, M. Torrisi and A. Valenti (Eds.), Kluwer Academic Publisher, Dordrecht, 1993
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© Copyright 1999
American Mathematical Society