Pointwise A-Priori Bounds for Strongly Coupled Semilinear Parabolic Systems

摘要

The prototype parabolic partial differential equation is the heat conduction equation. This paper deals with systems of parabolic equations. Such systems occur in many contexts in addition to heat conduction, e.g. biology, in nuclear reactor techniques, in economics, etc. Let the n-vector u denote the (unknown) solution of a system of n parabolic partial differential equations. An important question in the study of these systems is the boundedness of u. Many techniques and criteria have been developed to solve this problem if the system is weakly coupled, i.e. if the k sub th equation contains second order space derivatives of only u sub k, the k sub th component of u. If this is not the case, the system is said to be strongly coupled. In the paper, for a broad class of strongly coupled parabolic systems pointwise, boundedness of the solution u is established.