The heat equation with singular nonlinearity and singular initial data

We study the existence, uniqueness and regularity of positive solutions of the parabolic equation ut−Δu=a(x)uq+b(x)up in a bounded domain and with Dirichletʹs condition on the boundary. We consider here a Lα(Ω), b Lβ(Ω) and 00. We find a unique solution in the space .