ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A COUPLED SYSTEM OF MAXWELL'S EQUATIONS AND A CONTROLLED DIFFERENTIAL INCLUSION

作者：Kalinichenko Dina^*; Reitmann Volker; Skopinov Sergey

来源：Discrete and Continuous Dynamical Systems, 2013, 407-414.

• Asymptotic behavior
• evolutionary variational inequality
• stability
• dissipativity
• frequency-domain condition
• Maxwell's equation

The present article consists of two parts. In the first part we consider evolutionary variational inequalities with a nonlinearity which is described by a differential inclusion. Using the frequency-domain method we prove, under certain assumptions, the dissipativity of our variational inequality which is important for the asymptotic behavior of the system. In the second part a coupled system of Maxwell's equation and the heat equation is considered. For this system we introduce the notion of stability on a finite-time interval and present a theorem on this type of stability.

• 出版日期2013-11