%0 Journal Article %T A note on quasilinear parabolic systems in generalized spaces %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) %Z 2423-4788 %A Azroul, Elhoussine %A Balaadich, Farah %D 2021 %\ 01/01/2021 %V 7 %N 1 %P 86-95 %! A note on quasilinear parabolic systems in generalized spaces %K Quasilinear parabolic systems %K Orlicz-Sobolev spaces %K Young measures %R 10.22034/kjm.2020.211591.1660 %X We study the existence of solutions for quasilinear parabolic systems of the form \[\partial_tu-\text{div}\,\sigma(x,t,Du)=f\quad\text{in}\;Q=\Omega\times(0,T),\] whose right hand side belongs to $W^{-1,x}L_{\overline{M}}(Q;\R^m)$, supplemented with the conditions $u=0$ on $\partial\Omega\times(0,T)$ and $u(x,0)=u_0(x)$ in $\Omega$. By using a mild monotonicity condition for $\sigma$, namely strict quasimonotone, and the theory of Young measures, we deduce the needed result. %U https://www.kjm-math.org/article_123053_c7a14ce25359e34125f6f9f0a926b6b2.pdf