SIAM Journal on Control and Optimization, Vol.53, No.1, 475-500, 2015
OBSERVABILITY ESTIMATES AND NULL CONTROLLABILITY FOR FORWARD AND BACKWARD LINEAR STOCHASTIC KURAMOTO- SIVASHINSKY EQUATIONS
In this paper we discuss the observability estimates and the null controllability of forward and backward linear stochastic Kuramoto-Sivashinsky equations with random noise. The key point is to establish the Carleman estimates for stochastic fourth order forward and backward parabolic equations.
Keywords:forward and backward linear stochastic Kuramoto-Sivashinsky equations;observability estimate;null controllability;Carleman estimate