1
Department of Mathematics, Faculty of Sciences, Dhar El Mahraz FEZ
2
Departement of Mathematics, Faculty of Sciences, Dhar El Mahraz FEZ
10.22034/kjm.2020.211591.1660
Abstract
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.
Azroul, E., & Balaadich, F. (2021). A note on quasilinear parabolic systems in generalized spaces. Khayyam Journal of Mathematics, 7(1), 86-95. doi: 10.22034/kjm.2020.211591.1660
MLA
Elhoussine Azroul; Farah Balaadich. "A note on quasilinear parabolic systems in generalized spaces". Khayyam Journal of Mathematics, 7, 1, 2021, 86-95. doi: 10.22034/kjm.2020.211591.1660
HARVARD
Azroul, E., Balaadich, F. (2021). 'A note on quasilinear parabolic systems in generalized spaces', Khayyam Journal of Mathematics, 7(1), pp. 86-95. doi: 10.22034/kjm.2020.211591.1660
VANCOUVER
Azroul, E., Balaadich, F. A note on quasilinear parabolic systems in generalized spaces. Khayyam Journal of Mathematics, 2021; 7(1): 86-95. doi: 10.22034/kjm.2020.211591.1660
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