We study the homogeneous Dirichlet problem for the equation ut-div(F(z,∇u)∇u)=f,z=(x,t)∈QT=Ω×(0,T),where Ω ⊂ RN, is a bounded domain with ∂Ω ∈ C2, and F(z, ξ) = a(z) | ξ| p(z)-2+ b(z) | ξ| q(z)-2. The variable exponents ...