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 $\sigma$.
Azroul, E., & Balaadich, F. (2020). Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity. Khayyam Journal of Mathematics, 6(1), 57-72. https://doi.org/10.22034/kjm.2019.97170
MLA
Azroul, E., & Balaadich, F. "Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity", Khayyam Journal of Mathematics, 6, 1, 2020, 57-72. doi: 10.22034/kjm.2019.97170
HARVARD
Azroul E., Balaadich F. (2020). 'Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity', Khayyam Journal of Mathematics, 6(1), pp. 57-72. doi: 10.22034/kjm.2019.97170
CHICAGO
E. Azroul & F. Balaadich, "Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity," Khayyam Journal of Mathematics, 6 1 (2020): 57-72, doi: 10.22034/kjm.2019.97170
VANCOUVER
Azroul E., Balaadich F. Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity. Khayyam J. Math. 2020;6(1):57-72. doi: 10.22034/kjm.2019.97170
