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Diffusive waves in inhomogeneous media

Published online by Cambridge University Press:  20 January 2009

Paul C. Fife
Paul C. Fife
Affiliation:
Heriot–Watt University, Edinburgh, Scotland University of Utah, Salt Lake City, Utah, U.S.A.
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When the function f(u) is of “bistable type’, i.e. has two zeros h̲ and h+ at which f' is negative and (for simplicity) has only one other zero between them, then the constant functions u = h± are L∞-stable solutions of the nonlinear diffusion equation

In addition, there are travelling wave solutions u+(x, t) and u̲(x, t) which, if

connect h+ to h̲ in the sense that

the convergence being uniform on bounded x-intervals. These solutions are of the form

where U(z) is a monotone function (the wave's profile), U(±∞) = h±, and the velocity c is a specific positive number depending on the function f.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 2 , June 1989 , pp. 291 - 315
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCE

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