Thermal waves in an absorbing and convecting medium

Philip Rosenau*, Shoshana Kamin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The quasi-linear parabolic equation ∂tu = a∂xxuα + b∂xuβ - cuγ exhibits a wide variety of wave phenomena, some of which are studied in this work; and some solvable cases are presented. The motion of the wave front is characterized in terms of α, β and γ. Among the interesting phenomena we note the effect of fast absorption (b 0, 0 < γ < 1) that causes extinction within a finite time, may break the evolving pulse into several sub-pulses and causes the expanding front to reverse its direction. In the convecting case (c 0, b ≠ 0) propagation has many features in common with Burgers equation, α = 1; particularly, if 0 < a ≪ 1, a shock-like transit layer is formed.

Original languageEnglish
Pages (from-to)273-283
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Volume8
Issue number1-2
DOIs
StatePublished - Jul 1983

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