Some approaches to the control problem for diffusion chaos (Q2704011)

The behavior of solutions of some reaction-diffusion systems (these systems are used in modeling of diverse processes and phenomena in physics), after the loss of stability of the thermodynamic branch, are described by the Kuramoto-Tsuzuki equation NEWLINE\[NEWLINEW_t= (1+ ic_0)W+ (1+ ic_1)\Delta_xW- (1+ ic_2)W|W|^2,\tag{1}NEWLINE\]NEWLINE \(W\) is a complex-valued function, \(W(x,t)= u(x,t)+ iv(x,t)\), \(c_0\), \(c_1\), \(c_2\) are real constants.NEWLINENEWLINENEWLINESome boundary value problems with the equation (1), on a closed interval \([0,\ell]\), are considered; certain problems concerning the diffusion chaos are reduced to the stabilization of the zero solution of these problems; there is used a method which is developed in this paper.