Integral continuity and stability for stochastic hyperbolic equations. (English) Zbl 0777.35096

Continuous dependence of mild solutions of stochastic hyperbolic problems with respect to coefficients is investigated. Continuous dependence is meant in the sense of integral continuity which in some sense represents the best possible result on the continuous dependence of solutions for ODE with respect to the right hand-side.
The problem is considered for both bounded and unbounded time intervals. Some results on asymptotic stability are also established which are of independent interest.
The methods used in the paper are not restricted to hyperbolic systems only. They can also be applied to other equations.


35R60 PDEs with randomness, stochastic partial differential equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35L10 Second-order hyperbolic equations