Nonlinear thermal evolution in an inhomogeneous medium

Various simple transport models of electron temperature in a confined plasma are reducible to the quasilinear equation rho(x)u/sub t/ = [c(x)u/sup n//sub x/]/sub x/ +A(x)u/sup s/, -10. On the other hand, if R = infinity and A = 0 then the system becomes isothermalized: u→u-bar = ∫+1/sub -/1 u(x, 0) rho(x) dx/∫1/sub -/1 rho(x) dx>0. In such a case addition of heat sources will cause a thermal explosion