Quantitative analysis of hybrid parabolic systems with Markovian regime switching via practical stability

In this paper, the concept of practical stability is investigated for parabolic partial differential equations under Markovian switching. The concept of vector-Lyapunov-like functionals coupled with the comparison principle is utilized to establish sufficient conditions for various types of practical stability criteria in the pth moment and in probability of the equilibrium state of the system under Markovian regime switchings. An example is provided to demonstrate the obtained results.