Pullback D-Attractor of Coupled Rod Equations with Nonlinear Moving Heat Source

Abstract

We consider the pullback $D$-attractor for the nonautonomous nonlinear equations of thermoelastic coupled rod with a nonlinear moving heat source. By Galerkin method, the existence and uniqueness of global solutions are proved under homogeneous boundary conditions and initial conditions. By prior estimates combined with some inequality skills, the existence of the pullback $D$-absorbing set is obtained. By proving the properties of compactness about the nonlinear operator $g_1(·)$, $g_2(·)$, and then proving the pullback $D$-condition (C), the existence of the pullback $D$-attractor of the equations previously mentioned is given.