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

• El Houcine Rami ^[1] ; Elhoussine Azroul ^[1] ; Abdelkrim Barbara ^[1]
  1. [1] Universidad Sidi Mohamed Ben Abdellah
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 77, Nº. 4, 2020, págs. 507-529
• Idioma: inglés
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• Resumen

  • 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.