On the plate equation with nonstationary stochastic process coefficients

Abstract

AbstractIn mechanics, while investigating the vibration of plates, we are frequently confronted with random perturbations from both internal and external environments, such as inhomogeneous materials, unstable temperature fluctuation, etc. In this respect, the plate equation with stochastic coefficients is used for modeling the randomness from various perturbations. Current paper is concerned with the regularity behavior of the solution of the stochastic plate equation, in particular, the joint influence from the degenerating and oscillating coefficients on the principal operator is of prime consideration. We apply the sophisticated techniques from microlocal analysis and stochastic analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the estimates, appropriate counter‐examples with periodic coefficients are constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments.