TY - JOUR
ID - 97170
TI - Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity
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 Mehraz, B.P. 1796 Atlas, Fez-Morocco.
Y1 - 2020
PY - 2020
VL - 6
IS - 1
SP - 57
EP - 72
KW - Quasilinear parabolic systems
KW - weak monotonicity
KW - weak solution
KW - Young measures
DO - 10.22034/kjm.2019.97170
N2 - 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 $\sigma$.
UR - http://www.kjm-math.org/article_97170.html
L1 - http://www.kjm-math.org/article_97170_c50bb41e07dca9346043d4702bb0d0b2.pdf
ER -