Nonlinear Diffusion Problem Arising in Plasma Physics

James G. Berryman and Charles J. Holland
Phys. Rev. Lett. 40, 1720 – Published 26 June 1978
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Abstract

In earlier studies of plasma diffusion with Okuda-Dawson scaling (Dn12), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separable solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toward the separable solution is summarized. Rigorous bounds on the decay time are also presented.

  • Received 17 March 1978

DOI:https://doi.org/10.1103/PhysRevLett.40.1720

©1978 American Physical Society

Authors & Affiliations

James G. Berryman* and Charles J. Holland

  • Courant Institute of Mathematical Sciences, New York University, New York, New York 10012

  • *On leave from Continental Oil Company. Permanent address: Bell Laboratories, Whippany, N. J. 07981.
  • Permanent address: Department of Mathematics, Purdue University, West Lafayette, Ind. 47906.

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Vol. 40, Iss. 26 — 26 June 1978

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