Some existence and regularity results for porous media and fast diffusion equations with a gradient term

Original · EN

In this paper we consider the problem (P) {arrayrclll uₜ- uᵐ&=&| u|q +f(x,t),& u≥ 0 in Ωₜ≡ Ω× (0,T), u(x,t)&=&0 & on ∂Ω× (0,T) u(x,0)&=&u₀(x),& x∈ Ωarray. where Ø⊂, N≥ 2, is a bounded regular domain, 1<q≤ 2, and f≥ 0, u₀≥ 0 are in a suitable class of functions. We obtain some results for elliptic-parabolic problems with measure data related to problem (P) that we use to study the existence of solutions to problem (P) according with the values of the parameters q and m.