Observability Of Some Stochastic Coupled Degenerate Parabolic Systems

In this dissertation,the observability problem for a class of stochastic coupled degenerate parabolic systems is studied.The coupled system consists of two one-dimensional stochastic degenerate parabolic equations with different diffusion coefficients,both of which degenerate at the boundary point.The observation is the local information of one component of the solution on any non-empty open subset.By imposing suitable conditions on the coupling coefficients in drift and diffusion terms,the observability result of the system can be obtained,namely,the partial information of a solution component can uniquely determine the whole information of the solution to the coupled system.In order to obtain the above observability result,a new Carleman estimate is established for stochastic degenerate parabolic equations.When the problem considered in this dissertation degenerates to the deterministic case,the observability result requires the associated coupling coefficient in the drift term to satisfy suitable conditions.However,in the stochastic case,the observability result is still valid if only some conditions are proposed for the coupling coefficient in the diffusion term.