Qualitative properties of nonlinear parabolic operators II: the case of PDE systems

The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors' research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results.