On exponential stability criteria of stochastic partial differential equations

Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential equations are shown in this paper. In particular, the main results obtained in Caraballo and Real (1994, Stochast. Anal. Appl. 12(5), 517–525) are improved, since the new coercivity condition introduced in this work permits the state independent term γ to be time dependent and nonnegative but of subexponential growth, while in Caraballo and Real (1994) this parameter is required to be constant and nonpositive. Several examples are studied to illustrate the theory.