%0 Journal Article
%T Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
%Z 2423-4788
%A Azroul, Elhoussine
%A Balaadich, Farah
%D 2020
%\ 01/01/2020
%V 6
%N 1
%P 57-72
%! Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity
%K Quasilinear parabolic systems
%K weak monotonicity
%K weak solution
%K Young measures
%R 10.22034/kjm.2019.97170
%X The existence of solutions to the strongly quasilinear parabolic system\[\frac{\partial u}{\partial t}-\text{div}\,\sigma(x,t,u,Du)+g(x,t,u,Du)=f,\]is proved, where the source term $f$ is assumed to belong to $L^{p'}(0,T; W^{-1,p'}(\Omega;R^m))$. Further, we prove the existence of a weak solution by means of the Young measures under mild monotonicity assumptions on $\sigma$.
%U http://www.kjm-math.org/article_97170_c50bb41e07dca9346043d4702bb0d0b2.pdf