@article {
author = {Azroul, Elhoussine and Balaadich, Farah},
title = {Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {1},
pages = {57-72},
year = {2020},
publisher = {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)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2019.97170},
abstract = {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 $\sigma$.},
keywords = {Quasilinear parabolic systems,weak monotonicity,weak solution,Young measures},
url = {http://www.kjm-math.org/article_97170.html},
eprint = {http://www.kjm-math.org/article_97170_c50bb41e07dca9346043d4702bb0d0b2.pdf}
}