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Asymptotic stability in viscoelasticity. (English) Zbl 0214.24503

MSC:
74H55 Stability of dynamical problems in solid mechanics
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
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[1] Dafermos, C. M., An Abstract Volterra Equation with Applications to Linear Viscoelasticity. To appear in J. Diff. Equations. · Zbl 0212.45302
[2] Hale, J. K., J. Math. Anal. Applications 26, 39–59 (1969). · Zbl 0179.13303 · doi:10.1016/0022-247X(69)90175-9
[3] Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 6, 355–370 (1960). · Zbl 0097.16403 · doi:10.1007/BF00276168
[4] Coleman, B. D., & W. Noll, Rev. Mod. Phys. 33, 239–249 (1961). · Zbl 0103.40804 · doi:10.1103/RevModPhys.33.239
[5] Wang, C. C., Arch. Rational Mech. Anal. 18, 343–366 (1965). · Zbl 0125.41601 · doi:10.1007/BF00281325
[6] Kelley, J. L., General Topology. Princeton: D. Van Nostrand 1955.
[7] Coleman, B. D., & V. J. Mizel, Arch. Rational Mech. Anal. 23, 87–123 (1966). · Zbl 0146.46104 · doi:10.1007/BF00251727
[8] Coleman, B. D., & V. J. Mizel, Arch. Rational Mech. Anal. 30, 173–196 (1968). · Zbl 0184.36801 · doi:10.1007/BF00253873
[9] Dunford, N., & J. T. Schwartz, Linear Operators, Part I. New York: Interscience. · Zbl 0243.47001
[10] Slemrod, M., An Invariance Principle for Dynamical Systems in Hilbert Space with Applications to Asymptotic Stability of Equilibria. Thesis Submitted to the Division of Applied Mathematics, Brown University, June 1969.
[11] Dafermos, C. M., An Invariance Principle for Compact Processes. Pending Publication.
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