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1: 20.13 Physical Applications
with κ = - i π / 4 . For τ = i t , with α , t , z real, (20.13.1) takes the form of a real-time t diffusion equation …Theta-function solutions to the heat diffusion equation with simple boundary conditions are discussed in Lawden (1989, pp. 1–3), and with more general boundary conditions in Körner (1989, pp. 274–281). …
2: 28.33 Physical Applications
  • McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.

  • 3: Bibliography K
  • A. A. Kapaev (1988) Asymptotic behavior of the solutions of the Painlevé equation of the first kind. Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).
  • P. L. Kapitsa (1951a) Heat conduction and diffusion in a fluid medium with a periodic flow. I. Determination of the wave transfer coefficient in a tube, slot, and canal. Akad. Nauk SSSR. Žurnal Eksper. Teoret. Fiz. 21, pp. 964–978.
  • V. Kourganoff (1952) Basic Methods in Transfer Problems. Radiative Equilibrium and Neutron Diffusion. Oxford University Press, Oxford.
  • Y. A. Kravtsov (1964) Asymptotic solution of Maxwell’s equations near caustics. Izv. Vuz. Radiofiz. 7, pp. 1049–1056.
  • M. D. Kruskal (1974) The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.
  • 4: 10.73 Physical Applications
    §10.73(ii) Spherical Bessel Functions
    For applications of the Rayleigh function σ n ( ν ) 10.21(xiii)) to problems of heat conduction and diffusion in liquids see Kapitsa (1951a).