Elżanowski, Marek Thermodynamic stability of continuous body. (English) Zbl 0582.73006 J. Math. Anal. Appl. 108, 303-315 (1985). M. E. Gurtin [Arch. Rat. Mech. Anal. 59, 63-96 (1975; Zbl 0341.73003)], has been proposed a general stability theory of thermodynamics. In this paper the author extends Gurtin’s stability theory to the non-autonomous case. A slightly modified version of Gurtin’s theory of dynamical systems is presented, and some new sufficient conditions for Lyapunov stability of thermodynamical systems are proved. The paper is a real contribution towards bringing about a unified general theory of dynamical systems and a general stability theory of thermodynamics. Reviewer: Gh.Gr.Ciobanu MSC: 74A15 Thermodynamics in solid mechanics 70K20 Stability for nonlinear problems in mechanics 74A99 Generalities, axiomatics, foundations of continuum mechanics of solids 54H20 Topological dynamics (MSC2010) Keywords:Gurtin’s stability theory; non-autonomous case; Lyapunov stability of thermodynamical systems PDF BibTeX XML Cite \textit{M. Elżanowski}, J. Math. Anal. Appl. 108, 303--315 (1985; Zbl 0582.73006) Full Text: DOI References: [1] Ball, J.M, On the asymptotic behaviour of generalized processes, with applications to nonlinear evolution equations, J. differential equations, 27, 224-265, (1978) · Zbl 0376.35002 [2] Ball, J.M; Peletier, L.A, Global attraction for the one-dimensional heat equation with nonlinear time-dependent boundary conditions, Arch. rational mech. anal., 65, 193-201, (1977) · Zbl 0363.35014 [3] Elżanowski, M, On necessary conditions for stability in thermodynamics, Bull. acad. polon. sci. Sér. sci. tech., 28, 1–2, 77-83, (1980) [4] Ericksen, J.L, Thermodynamic stability, (), 187-193 [5] Gurtin, M.E, Thermodynamics and the energy criterion for stability, Arch. rational mech. anal., 52, 93-103, (1973) · Zbl 0275.73030 [6] Gurtin, M.E, Thermodynamics and stability, Arch. rational mech. anal., 59, 63-96, (1975) · Zbl 0341.73003 [7] Hale, J.K, Dynamical systems and stability, J. math. anal. appl., 26, 39-59, (1969) · Zbl 0179.13303 [8] LaSalle, J.P, An invariance principle in the theory of stability, (), 277-285 · Zbl 0183.09401 [9] Infante, E.F, Some results and applications of generalized dynamical systems, (), 91-105 · Zbl 0231.93021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.