One approach to study of stability of integro-differential equations

A method was proposed to reduce intergo-differential equations to a system of ordinary differential equations. Linear approximations were used to analyze the stability of integro-differential equations and nonlinear systems. The linearized phase transition model was analyzed to study the problem of memory effects in phase transitions. The analysis of the Gutrin-Pipkin type energy balance equation with phase relaxation equation showed that the obtained trivial solutions were asymptotically stable.