Initial trace of solutions of some quasilinear parabolic equations with absorption (Q1849067)

There is studied the existence of an initial trace of nonnegative solutions of the equation \[ u_t-\nabla\big(|\nabla u|^{p-2}\nabla u\big)+ u^q=0 \;\;\text{in} \;\;Q_T=\Omega\times(0,T) \] with \(p>1, q>0\). There is proved that the initial trace is an outer regular Borel measure which may not be locally bounded for some values of the parameters \(p\) and \(q\). There is investigated also the solvability of the corresponding Cauchy problem with a given generalized Borel measure as initial data.