×

zbMATH — the first resource for mathematics

Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity. (English) Zbl 0498.35015

MSC:
35B45 A priori estimates in context of PDEs
35K55 Nonlinear parabolic equations
35L60 First-order nonlinear hyperbolic equations
74A15 Thermodynamics in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Andrews, G., On the existence of solutions to the equation utt = uxxt + σ(ux)x, J. diff. eqns, 35, 200-231, (1980)
[2] Dafermos, C.M., The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity, J. diff. eqns, 6, 71-86, (1969) · Zbl 0218.73054
[3] Friedman, A., Partial differential equations of parabolic type, (1964), Prentice Hall Englewood Cliffs, NJ · Zbl 0144.34903
[4] Greenberg, J.M.; Maccamy, R.C.; Mizel, V.J., On the existence, uniqueness, and stability of solutions to the equation σ(ux)uxx + λuxtx = ϱ0utt, J. math. mech., 17, 707-728, (1968) · Zbl 0157.41003
[5] Kazhykhov, A.V., Sur la solubilité globale des problèmes monodimensionnels aux valeurs initiales-limitées pour LES équations d’un gaz visqueux et calorifère, C.r. hebd. Séanc. acad. sci. Paris, 284, 317-320, (1977), Sér. A · Zbl 0355.35071
[6] Kazhikhov, A.V.; Shelukhin, V.V.; Kazhikhov, A.V.; Shelukhin, V.V., Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, Pmm, Appl. math. mech., 41, 273-282, (1977), English translation
[7] Ladyženskaja, O.A.; Solonnikov, V.A.; Ural’ceva, N.N., Linear and quasilinear equations of parabolic type, (1968), American Math. Society Providence, RI, (Translated from the Russian by S. Smith)
[8] Matsumura, A.; Nishida, T., The initial value problem for the equations of motion of viscous and heat-conductive gases, J. math. Kyoto univ., 20, 67-104, (1980) · Zbl 0429.76040
[9] Protter, M.H.; Weinberger, H.F., Maximum principles in differential equations, (1967), Prentice Hall Englewood Cliffs, NJ · Zbl 0153.13602
[10] Slemrod, M., Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity, Arch. rat. mech. analysis, 76, 97-133, (1981) · Zbl 0481.73009
[11] Dafermos, C.M., Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. math. analysis, 13, (1982) · Zbl 0489.73124
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.