TY - JOUR
T1 - Thermal waves in an absorbing and convecting medium
AU - Rosenau, Philip
AU - Kamin, Shoshana
N1 - Funding Information:
The second term on the right-hand side describes volumetric absorption, which in the case of a plasma is caused by radiation to which plasma is transparent (V =0.5 in the case of Bremsstrahlung). For synchrontron radiation, 1.5 ~< y ~< 2; the exact value depends on the amount * This work was partially supported by U.S. Air Force contracts AFOSR-76-2881 and AFOSR-78-3602.
PY - 1983/7
Y1 - 1983/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0001632479&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(83)90325-1
DO - 10.1016/0167-2789(83)90325-1
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AN - SCOPUS:0001632479
SN - 0167-2789
VL - 8
SP - 273
EP - 283
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-2
ER -