TY - JOUR ID - 123053 TI - A note on quasilinear parabolic systems in generalized spaces JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Azroul, Elhoussine AU - Balaadich, Farah AD - Department of Mathematics, Faculty of Sciences, Dhar El Mahraz FEZ AD - Departement of Mathematics, Faculty of Sciences, Dhar El Mahraz FEZ Y1 - 2021 PY - 2021 VL - 7 IS - 1 SP - 86 EP - 95 KW - Quasilinear parabolic systems KW - Orlicz-Sobolev spaces KW - Young measures DO - 10.22034/kjm.2020.211591.1660 N2 - 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. UR - https://www.kjm-math.org/article_123053.html L1 - https://www.kjm-math.org/article_123053_c7a14ce25359e34125f6f9f0a926b6b2.pdf ER -