Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity

[摘要] 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 $\sigma$.

[学科分类] 公共、环境与职业健康