Resumen de Existence of solutions for some quasilinear parabolic systems with weight and weak monotonicity general data

Rami El Houcine, Elhoussine Azroul, Abdelkrim Barbara

• We prove the existence of weak solution u for the nonlinear parabolic systems:

  (QPS)ω⎧⎩⎨⎪⎪∂tu−divσ(x,t,u,Du)u(x,t)u(x,0)===v(x,t)+f(x,t,u,Du)+divg(x,t,u) in ΩT0 on ∂Ω×(0,T)u0(x) on Ω which is a Dirichlet Problem. In this system, v belongs to Lp′(0,T,W−1,p′(Ω,ω∗,Rm)) and u0∈L2(Ω,ω0,Rm), f and g satisfy some standards continuity and growth conditions. We prove existence of a weak solution of different variants of this system under classical regularity for some ps∈]2nn+2;∞[, growth and coercivity for σ but with only very mild monotonicity assumptions.