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Hyperbolic type transport equations

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  • García-Colín, L.S.
  • Olivares-Robles, M.A.

Abstract

In recent years hyperbolic type transport equations have acquired a great deal of importance in problems ranging from theoretical physics to biology. In spite of their greater mathematical difficulty as compared with their parabolic type analogs arising from the framework of Linear Irreversible Thermodynamics, they have, in many ways, superseded the latter ones. Although the use of this type of equations is well known since the last century through the telegraphist equation of electromagnetic theory, their use in studying several problems in transport theory is hardly fifty years old. In fact the first appearance of a hyperbolic type transport equation for the problem of heat conduction dates back to Cattaneos' work in 1948. Three years later, in 1951 S. Goldstein showed how in the theory of stochastic processes this type of an equation is obtained in the continuous limit of a one-dimensional persistent random walk problem. After that, other phenomenological derivations have been offered for such equations.

Suggested Citation

  • García-Colín, L.S. & Olivares-Robles, M.A., 1995. "Hyperbolic type transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(1), pages 165-172.
    • Handle: RePEc:eee:phsmap:v:220:y:1995:i:1:p:165-172
    DOI: 10.1016/0378-4371(95)00122-N
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    Cited by:

    1. Povstenko, Y.Z., 2010. "Evolution of the initial box-signal for time-fractional diffusion–wave equation in a case of different spatial dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4696-4707.

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