LYAPUNOV FUNCTION OF SEMI-GROUPS GENERATED BY A CLASS OF SOBOLEV TYPE EQUATIONS - Mamikonyan, H. A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2023)
In this paper Lyapunov function the following initial boundary value problem for a class of Sobolev type equations is consideredcases A(ut)+Bu=0, u|_t=0=u_0, u|_Σ=0, cases where A and B are nonlinear operators of the following form: Au=-^n_i,j=1x_ia_j(x,u, riangledown u), Bu= -^n_i,j=1x_ib_j (x,u, riangledown u). The existence of Lyapunov function on the attractor of the semi-group generated by this equation is proved. It is given the construction of attractor by the fixed points of that semi-group.