Initial Trace of Solutions of Some Quasilinear Parabolic Equations with Absorption

We study the existence of an initial trace of nonnegative solutions of the problemδtu−∇·(∣∇u∣p−2∇u)+uq=0in QT=Ω×(0,T). We prove that the initial trace is an outer regular Borel measure which may not be locally bounded for some values of the parameters p and q. We study also the corresponding Cauchy problems with a given generalized Borel measure as initial data.