Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
Youssef Akdim, Abdelmoujib Benkirane, Mostafa El Moumni, Hicham Redwane · Georgian Mathematical Journal · 2016
Abstract We study the existence result of a renormalized solution for a class of nonlinear parabolic equations of the form ∂ b ( x , u ) ∂ t - div ( a ( x , t , u , ∇ u ) ) + g ( x , t , u , ∇ u ) + H ( x , t , ∇ u ) = μ in Ω × ( 0 , T ) , ${\partial b(x,u)\over\partial t}-\operatorname{div}(a(x,t,u, abla u))+g(x,t,u% , abla u)+H(x,t, abla u)=\mu\quad\text{in }\Omega\times(0,T),$ where the right-hand side belongs to L 1 ( Q T ) + L p ′ ( 0 , T ; W - 1 , p ′ ( Ω