Nonnegative solutions of degenerating quasilinear parabolic equations with measurable coefficients (Q1594139)

It is studied the behavior of nonnegative solutions to equations of the form \[ {\partial u\over \partial t} - \sum_{i=1}^N {d\over d x_i} a_i\big(x,t,{\partial u\over \partial x} \big) =f(x,t), \] where \((x,t)\in {\mathbb{R}}^N\times (0,T),\) \(0<T<\infty,\) and the coefficients supposed to be Caratheódory's functions. It is studied the behavior of nonnegative solutions when \(|x|\to \infty\) and \(t\to 0.\)