Previous |  Up |  Next

Article

References:
[1] G. Andrews: On the existence of solutions to the equation $u\sb{tt}=u\sb{xxt}+\sigma (u\sb{x})\sb{x}$. J. Differential Eq. 35 (1980), 200-231. MR 0561978
[2] G. Andrews J. M. Ball: Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity. J. Differential Eq. 44 (1982), 306-341. DOI 10.1016/0022-0396(82)90019-5 | MR 0657784
[3] R. Arima Y. Hasegawa: On global solutions for mixed problem of semi-linear differential equation. Proc. Japan. Acad. 39 (1963), 721-725. MR 0161046
[4] T. K. Caughey J. Ellison: Existence, uniqueness and stability of solutions of a class of nonlinear partial differential equations. J. Math. Anal. Appl. 51 (1975), 1 - 32. DOI 10.1016/0022-247X(75)90136-5 | MR 0387801
[5] J. С. Clements: Existence theorems for a quasilinear evolution equation. SIAM J. Appl. Math. 26 (1974), 745-752. DOI 10.1137/0126066 | MR 0372426 | Zbl 0252.35044
[6] J. С. Clements: On the existence and uniqueness of solutions of the equation $u\sb{tt}-\partial \sigma \sb{i}(u\sb{x\sb{i}})/\partial x\sb{i}-D\sb{N}u\sb{t}=f$. Canad. Math. Bull. 18 (1975), 181-187. MR 0397200
[7] С. M. Dafermos: The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity. J. Differential Eq. 6 (1969), 71 - 86. DOI 10.1016/0022-0396(69)90118-1 | MR 0241831 | Zbl 0218.73054
[8] P. L. Davis: A quasilinear hyperbolic and related third-order equations. J. Math. Anal. Appl. 51 (1975), 596-606. DOI 10.1016/0022-247X(75)90110-9 | MR 0390514 | Zbl 0312.35018
[9] Y. Ebihara: On some nonlinear evolution equations with the strong dissipation. J. Differential Eq. 30 (1978), 149-164, II, ibid. 34 (1979), 339-352. DOI 10.1016/0022-0396(78)90011-6 | MR 0513267
[10] Y. Ebihara: Some evolution equations with the quasi-linear strong dissipation. J. Math. Pures et Appl. 58 (1979), 229-245. MR 0539221 | Zbl 0405.35049
[11] Y. Ebihara: Some evolution equations with linear and quasi-linear strong dissipation. J. Gen. Res. Inst. Fukuoka Univ. 66 (1983), 7-19. MR 0730317 | Zbl 0536.35052
[12] W. M. Ewing W. S. Jardetzky F. Press: Elastic waves in layered media. McGraw-Hill series in the geological sciences, New York-Toronto-London 1957. MR 0094967
[13] W. E. Fitzgibbon: Strongly damped quasilinear evolution equations. J. Math. Anal. Appl. 79 (1981), 536-550. DOI 10.1016/0022-247X(81)90043-3 | MR 0606499 | Zbl 0476.35040
[14] J. M. Greenberg: On the existence, uniqueness, and stability of solutions of the equation $\rho \sb{0}{\germ X}\sb{tt}=E({\germ X}\sb{x}) {\germ X}\sb{xx}+\lambda {\germ X}\sb{xxt}$. J. Math. Anal. Appl. 25 (1969), 575-591. MR 0240473
[15] J. M. Greenberg R. C. MacCamy: On the exponential stability of solutions of $E(u\sb{x})u\sb{xx}+\lambda u\sb{xtx}=\rho u\sb{tt}$. J. Math. Anal. Appl. 31 (1970), 406-417. MR 0273178
[16] J. M. Greenberg R. C. MacCamy V. S. Mizel: On the existence, uniqueness, and stability of solutions of the equation $\sigma \sp{\prime} \,(u\sb{x})u\sb{xx}+\lambda u\sb{xtx}=\rho \sb{0}u\sb{tt}$. J. Math. Mech. 17 (1968), 707-728. MR 0225026
[17] A. Haraux: Nonlinear evolution equations - global behavior of solutions. Lecture Notes in Mathematics Vol. 841, Springer-Verlag, Berlin- Heidelberg-New York 1981. DOI 10.1007/BFb0089606 | MR 0610796 | Zbl 0461.35002
[18] L. Herrmann: Periodic solutions of a strongly nonlinear wave equation with internal friction. (Czech.) Thesis, Prague 1977, 30 pp.
[19] L. Herrmann: Periodic solutions of abstract differential equations: the Fourier method. Czechoslovak Math. J. 30 (1980), 177-206. MR 0566046 | Zbl 0445.35013
[20] T. Kakita: Time-periodic solutions of some non-linear evolution equations. Publ. Res. Inst. Math. Sci 9 (1973/74), 477-492. DOI 10.2977/prims/1195192568 | MR 0342868
[21] H. Kolsky: Stress waves in Solids. Clarendon Press, Oxford 1953. Zbl 0052.42502
[22] A. I. Kozhanov: An initial-boundary value problem for a class of equations of non-classical type. (Russian.) Differenciaľnye Uravn. 15 (1979), 272-280. (English trans., in: Differential Equations 15 (1979), 186-191.)
[23] A. I. Kozhanov N. A. Lar'kin N. N. Janenko: On a regularization of equations of variable type. (Russian.) Dokl. Akad. Nauk SSSR 252 (1980), 525-527. (English trans., in: Soviet Math. Dokl. 21 (1980), 758-761.) MR 0577831
[24] P. A. Lagerstrom J. D. Cole L. Trilling: Problems in the theory of viscous compressible fluids. California Institute of Technology 1949. MR 0041617
[25] J.-L. Lions: Equations différentielles opérationnelles et problèmes aux limites. Springer-Verlag, Berlin-Göttingen-Heidelberg 1961. MR 0153974 | Zbl 0098.31101
[26] J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris 1969. MR 0259693 | Zbl 0189.40603
[27] J.-L. Lions E. Magenes: Problèrnes aux limites non homogènes et applications I, III. Dunod, Paris 1968.
[28] V. Lovicar: Theorem of Fréchet and asymptotically almost periodic solutions of some nonlinear equations of hyperbolic type. Nonlinear evolution equations and potential theory. Proc. of a Summer School held in September 1973 at Podhradí near Ledeč on Sázava. Ed. Josef Král. Academia, Prague 1975. MR 0481401
[29] R. C. MacCamy V. C. Mizel: Existence and non-existence in the large of solutions of quasilinear wave equations. Arch. Rational Mech. Anal. 25 (1967), 299-320. DOI 10.1007/BF00250932 | MR 0216165
[30] E. J. McShane: Integration. Princeton University Press 1947. MR 0082536 | Zbl 0033.05302
[31] H. Pecher: On global regular solutions of third order partial differential equations. J. Math. Anal. Appl. 73 (1980), 278-299. DOI 10.1016/0022-247X(80)90033-5 | MR 0560948 | Zbl 0429.35057
[32] M. A. Prestel: Forced oscillations for the solutions of a nonlinear hyperbolic equation. Nonlinear Anal. 6 (1982), 209-216. DOI 10.1016/0362-546X(82)90089-X | MR 0654313 | Zbl 0504.35065
[33] C. O. A. Sowunmi: On the existence of periodic solutions of the equation $\rho \sb{tt}u-(\sigma (u\sb{x}))\sb{x}-\lambda u\sb{xtx}-f=0$. Rend. Ist. Mat. Univ. Trieste 8 (1976), 58-68. MR 0430486
[34] I. Straškraba O. Vejvoda: Periodic solutions to abstract differential equations. Czechoslovak Math. J. 23 (1973), 635-669, 27 (1977), 511-513. MR 0499577
[35] A. E. Taylor: Introduction to functional analysis. J. Wiley and Sons, Inc., New York 1958. MR 0098966 | Zbl 0081.10202
[36] M. Tsutsumi: Some nonlinear evolution equations of second order. Proc. Japan Acad. 47 (1971), 950-955. MR 0312023 | Zbl 0258.35017
[37] G. F. Webb: Existence and asymptotic behavior for a strongly damped nonlinear wave equation. Canad. J. Math. 32 (1980), 631-643. DOI 10.4153/CJM-1980-049-5 | MR 0586981 | Zbl 0414.35046
[38] Y. Yamada: Note on certain nonlinear evolution equations of second order. Proc. Japan Acad. 55 (1979), 167-171. MR 0533540 | Zbl 0436.47054
[39] Y. Yamada: Some remarks on the equation $y\sb{tt}-\sigma (y\sb{x})$ $y\sb{xx}-y\sb{xtx}=f$. Osaka J. Math. 17 (1980), 303-323. MR 0587752
[40] Y. Yamada: Quasilinear wave equations and related nonlinear evolution equations. Nagoya Math. J. 84(1981), 31-83. DOI 10.1017/S0027763000019553 | MR 0641147 | Zbl 0472.35052
Partner of
EuDML logo