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\(p\)th moment exponential stability of hybrid stochastic fourth-order parabolic equations. (English) Zbl 1419.60055

Summary: We are concerned with a class of hybrid stochastic fourth-order parabolic equations with Markov switching in an infinite state space. By employing the fixed point theory we study the existence, uniqueness and \(p\)th moment exponential stability of the mild solution. Finally, we provide two examples to verify the effectiveness of our results.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
35K30 Initial value problems for higher-order parabolic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35K25 Higher-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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