One approach to study of stability of integro-differential equations

A. Domoshnitsky; Ya Goltser

doi:10.1016/S0362-546X(01)00508-9

One approach to study of stability of integro-differential equations

Department of Mathematics

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17 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	3885-3896
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	47
Issue number	6
DOIs	https://doi.org/10.1016/S0362-546X(01)00508-9
State	Published - Aug 2001

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title = "One approach to study of stability of integro-differential equations",

abstract = "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.",

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AB - 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.

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JO - Nonlinear Analysis, Theory, Methods and Applications

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One approach to study of stability of integro-differential equations

Abstract

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