Nature of heat propagation in nonlinear media with significantly nonstationary properties (Q1075516)

The author considers the Cauchy problem \[ (i)\quad [p(x,t)(u^ m)_ x]-q(x,t)u^ n-u_ t=0,\quad u(0,x)=u_ 0(x) \] \((t\geq 0,x\in {\mathbb{R}}^ 1)\) where \(m>1\), \(n>0\), \(p(x,t)>0\), \(u_ 0\geq 0\). Some theorems about global solvability of (i) and the localization of its generalized solution are given.