Maximum principles for weakly coupled parabolic systems

Abstract

Maximum principles and bounds for solutions of weakly coupled second order parabolic systems, Mu + Cu = 0 or f in

(n>1) are established by using the idea of Liapunov's Second Method. Here

is a second order real parabolic operator, and the m×l vectors f, u, and the mxm matrix C all have entries which are complex-valued functions.

Keywords:

• Maximum principles
• second order
• weakly coupled
• parabolic systems
• Liapunov's second method

AMS:

• 35B50
• 35K40