Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)Khayyam Journal of Mathematics2423-47886120200101Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity57729717010.22034/kjm.2019.97170ENElhoussine AzroulDepartment of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco.Farah BalaadichDepartment of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco.Journal Article20181205The existence of solutions to the strongly quasilinear parabolic system<br />\[\frac{\partial u}{\partial t}-\text{div}\,\sigma(x,t,u,Du)+g(x,t,u,Du)=f,\]<br />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 $\sigma$.https://www.kjm-math.org/article_97170_c50bb41e07dca9346043d4702bb0d0b2.pdf