[Show abstract][Hide abstract] ABSTRACT: Certain Lie algebras, represented as linear partial differential operators of first order, are used to derive autonomous systems of differential equations which involve limit cycles. To illustrate the approach an example is given.
No preview · Article · Aug 1977 · International Journal of Theoretical Physics
[Show abstract][Hide abstract] ABSTRACT: The presence of fluids in earth materials causes the propagation of fractures, which is observed on large scales to be regulated
by nonlinear diffusion processes. In contrast with linear diffusion processes, nonlinear diffusion can result in flows with
a pulse-like character (i.e., the fluid is confined to a finite space) whose profiles remain unchanged in time and which possess
either self-similar or traveling-wave characters. Entropy-like (Lyapunov functional) arguments are developed here to demonstrate
the asymptotic trend to self-similarity or traveling-waves in a broad class of nonlinear diffusion problems.
No preview · Article · May 1983 · Pure and Applied Geophysics
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