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The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity. (English) Zbl 0218.73054


MSC:

74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
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[1] Lax, P.D, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. math. phys., 5, 611-613, (1964) · Zbl 0135.15101
[2] MacCamy, R.C; Mizel, V.J, Existence and nonexistence in the large of solutions of quasilinear wave equations, Arch. rational mech. anal., 25, 299-320, (1967) · Zbl 0146.33801
[3] Greenberg, J.M; MacCamy, R.C; Mizel, V.J, On the existence, uniqueness, and stability of solutions of the equation σ′(ux) uxx + λuxtx = ϱ0utt, J. math. mech., 17, 707-728, (1968) · Zbl 0157.41003
[4] Hartman, P, Ordinary differential equations, (1964), John Wiley New York · Zbl 0125.32102
[5] Friedman, A, Partial differential equations of parabolic type, (1964), Prentice Hall Englewood Cliffs, New Jersey · Zbl 0144.34903
[6] Ladyženskaja, O.A; Ural’ceva, N.N; Ladyženskaja, O.A; Ural’ceva, N.N; Ladyženskaja, O.A; Ural’ceva, N.N, Boundary problems for linear and quasilinear parabolic equations, Izv. akad. nauk SSSR, ser. mat., Izv. akad. nauk SSSR, ser. mat., A.M.S. translations, ser. 2, 47, 217-299, (1965), English translation in
[7] Leray, J; Schauder, J, Topologie et équations fonctionnelles, Ann. sci. l’école norm. sup., 51, 45-78, (1934) · JFM 60.0322.02
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