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Abstract hyperbolic integrodifferential equations. (English) Zbl 0506.45016

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
74Hxx Dynamical problems in solid mechanics
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[1] Dafermos, C, An abstract Volterra equation with applications linear viscoelasticity, J. differential equations, 7, 554-569, (1970) · Zbl 0212.45302
[2] Dafermos, C, Asymptotic stability in viscoelasticity, Arch. rational mech. anal., 37, 297-308, (1970) · Zbl 0214.24503
[3] Dafermos, C; Nohel, J, Energy methods for nonlinear hyperbolic Volterra integrodifferential equations, () · Zbl 0464.45009
[4] Fitzgibbon, W, Nonlinear Volterra equation with infinite delay, Monatsh. math., 84, 275-288, (1977) · Zbl 0382.45003
[5] Fitzgibbon, W, Stability for abstract nonlinear Volterra equations involving finite delaÿ, J. math. anal. appl., 60, 429-434, (1977)
[6] {\scW. Fitzgibbon}, Semilinear integrodifferential equations in Banach space, J. Nonlinear Analysis, in press. · Zbl 0442.45014
[7] Friedman, A, Partial differential equations, (1969), Holt, Rinehart & Winston New York
[8] Goldstein, J, Semigroups of operators and abstract Cauchy problems, () · Zbl 0219.47037
[9] {\scM. Heard}, An abstract semilinear hyperbolic Volterra integrodifferential equation, to appear. · Zbl 0468.45010
[10] Kato, T, Perturbation theory for linear operators, (1966), Springer-Verlag New York · Zbl 0148.12601
[11] {\scT. Kato}, Quasilinear equations of evolution with applications to partial differential equations, Spectral Theory and Differential Equations, Springer Lecture Notes 448, 25-70.
[12] Lax, P, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. math. phys., 5, 611-613, (1964) · Zbl 0135.15101
[13] MacCamy, R, An integrodifferential equation with applications in heat flow, Q. appl. math., 35, 1-19, (1977)
[14] MacCamy, R, A model for one dimensional nonlinear viscoelasticity, Q. appl. math., 35, 21-33, (1977) · Zbl 0355.73041
[15] Nunziato, J, On heat conduction in materials with memory, Q. appl. math., 29, 187-204, (1971) · Zbl 0227.73011
[16] Pazy, A, Semigroups of linear operators and applications to partial differential equations, () · Zbl 0516.47023
[17] Travis, C; Webb, G, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. math. anal., 10, 412-424, (1979) · Zbl 0406.45014
[18] Travis, C; Webb, G, Existence and stability for partial functional differential equations, Trans. amer. math. soc., 200, 395-418, (1974) · Zbl 0299.35085
[19] Webb, G, An abstract semilinear Volterra integrodifferential equations, (), 255-260 · Zbl 0388.45012
[20] {\scG. Webb}, “A class of reaction-diffusion equations, in “Proceedings Int. Conf. on Volterra Equations, Helsinki,” Lecture Notes in Mathematics, Springer-Verlag, Berlin/New York, in press.
[21] Webb, G, Volterra integral equations and nonlinear semigroups, Nonlinear analysis: IMA, 1, 415-427, (1977) · Zbl 0364.45007
[22] Sobolevskii, P, Equations of parabolic type in Banach space, Amer. math. soc. trans. ser. 2, 49, 1-62, (1962)
[23] Finn, J; Wheeler, L, Wave propagation aspects of the generalized theory of heat conduction, Z. angew. math. phys., 23, 927-940, (1972) · Zbl 0249.35034
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