"Using the theory of Young measures, we prove existence solutions to a strongly quasilinear parabolic system \[\frac{\partial u}{\partial t}+A(u)=f,\] where $A(u)=-\text{div}\,\sigma(x,t,u,Du)+\sigma_0(x,t,u,Du)$, $\sigma(x,t,u,Du)$ and $\sigma_0(x,t,u,Du)$ are satisfy some conditions $f\in L^{p'}(0,T;W^{-1,p'}(\Omega;\R^m))$."

in this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. in the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. error estimates were also obtaine...

In this paper we apply methods of commutative algebra to analysis of systems of PDEs. More precisely, we show that systems which are parabolic in a generalized sense are equivalent to certain completed systems which are parabolic in the standard sense. We also propose a constructive method to get this completion, and Gröbner basis methods, via symbol modules of the systems, play a central role ...

Almost all of the 26 sporadic finite simple groups possess systems of subgroups which, in several ways, resemble the parabolic systems of the finite simple groups of Lie type. Many of these systems are catalogued in [RSt, RSm]. Those in [RSt] mirror more closely the minimal parabolic systems of a finite simple group of Lie type. In this paper the term minimal parabolic system will be used in a ...