Initial trace of solutions for a doubly nonlinear degenerate parabolic equations

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div(∇um|p-2∇um)+uq=0inQT=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 parameters p,q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.