Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation
Czechoslovak Mathematical Journal (1985)
- Volume: 35, Issue: 2, page 278-294
- ISSN: 0011-4642
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topHerrmann, Leopold. "Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation." Czechoslovak Mathematical Journal 35.2 (1985): 278-294. <http://eudml.org/doc/13511>.
@article{Herrmann1985,
author = {Herrmann, Leopold},
journal = {Czechoslovak Mathematical Journal},
keywords = {Time-periodic solutions; wave propagation; diffusion; exponential decay; semigroup; existence of weak -periodic solutions},
language = {eng},
number = {2},
pages = {278-294},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation},
url = {http://eudml.org/doc/13511},
volume = {35},
year = {1985},
}
TY - JOUR
AU - Herrmann, Leopold
TI - Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation
JO - Czechoslovak Mathematical Journal
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 2
SP - 278
EP - 294
LA - eng
KW - Time-periodic solutions; wave propagation; diffusion; exponential decay; semigroup; existence of weak -periodic solutions
UR - http://eudml.org/doc/13511
ER -
References
top- G. Andrews, On the existence of solutions to the equation , J. Differential Eq. 35 (1980), 200-231. (1980) MR0561978
- G. Andrews J. M. Ball, 10.1016/0022-0396(82)90019-5, J. Differential Eq. 44 (1982), 306-341. (1982) MR0657784DOI10.1016/0022-0396(82)90019-5
- R. Arima Y. Hasegawa, On global solutions for mixed problem of semi-linear differential equation, Proc. Japan. Acad. 39 (1963), 721-725. (1963) MR0161046
- T. K. Caughey J. Ellison, 10.1016/0022-247X(75)90136-5, J. Math. Anal. Appl. 51 (1975), 1 - 32. (1975) MR0387801DOI10.1016/0022-247X(75)90136-5
- J. С. Clements, 10.1137/0126066, SIAM J. Appl. Math. 26 (1974), 745-752. (1974) Zbl0252.35044MR0372426DOI10.1137/0126066
- J. С. Clements, On the existence and uniqueness of solutions of the equation , Canad. Math. Bull. 18 (1975), 181-187. (1975) MR0397200
- С. M. Dafermos, 10.1016/0022-0396(69)90118-1, J. Differential Eq. 6 (1969), 71 - 86. (1969) Zbl0218.73054MR0241831DOI10.1016/0022-0396(69)90118-1
- P. L. Davis, 10.1016/0022-247X(75)90110-9, J. Math. Anal. Appl. 51 (1975), 596-606. (1975) Zbl0312.35018MR0390514DOI10.1016/0022-247X(75)90110-9
- Y. Ebihara, 10.1016/0022-0396(78)90011-6, J. Differential Eq. 30 (1978), 149-164, II, ibid. 34 (1979), 339-352. (1978) MR0513267DOI10.1016/0022-0396(78)90011-6
- Y. Ebihara, Some evolution equations with the quasi-linear strong dissipation, J. Math. Pures et Appl. 58 (1979), 229-245. (1979) Zbl0405.35049MR0539221
- Y. Ebihara, Some evolution equations with linear and quasi-linear strong dissipation, J. Gen. Res. Inst. Fukuoka Univ. 66 (1983), 7-19. (1983) Zbl0536.35052MR0730317
- 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. (1957) MR0094967
- W. E. Fitzgibbon, 10.1016/0022-247X(81)90043-3, J. Math. Anal. Appl. 79 (1981), 536-550. (1981) Zbl0476.35040MR0606499DOI10.1016/0022-247X(81)90043-3
- J. M. Greenberg, On the existence, uniqueness, and stability of solutions of the equation , J. Math. Anal. Appl. 25 (1969), 575-591. (1969) MR0240473
- J. M. Greenberg R. C. MacCamy, On the exponential stability of solutions of , J. Math. Anal. Appl. 31 (1970), 406-417. (1970) MR0273178
- J. M. Greenberg R. C. MacCamy V. S. Mizel, On the existence, uniqueness, and stability of solutions of the equation , J. Math. Mech. 17 (1968), 707-728. (1968) MR0225026
- A. Haraux, 10.1007/BFb0089606, Lecture Notes in Mathematics Vol. 841, Springer-Verlag, Berlin- Heidelberg-New York 1981. (1981) Zbl0461.35002MR0610796DOI10.1007/BFb0089606
- L. Herrmann, Periodic solutions of a strongly nonlinear wave equation with internal friction, (Czech.) Thesis, Prague 1977, 30 pp. (1977)
- L. Herrmann, Periodic solutions of abstract differential equations: the Fourier method, Czechoslovak Math. J. 30 (1980), 177-206. (1980) Zbl0445.35013MR0566046
- T. Kakita, 10.2977/prims/1195192568, Publ. Res. Inst. Math. Sci 9 (1973/74), 477-492. (1973) MR0342868DOI10.2977/prims/1195192568
- H. Kolsky, Stress waves in Solids, Clarendon Press, Oxford 1953. (1953) Zbl0052.42502
- 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.) (1979)
- 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.) (1980) MR0577831
- P. A. Lagerstrom J. D. Cole L. Trilling, Problems in the theory of viscous compressible fluids, California Institute of Technology 1949. (1949) MR0041617
- J.-L. Lions, Equations différentielles opérationnelles et problèmes aux limites, Springer-Verlag, Berlin-Göttingen-Heidelberg 1961. (1961) Zbl0098.31101MR0153974
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969. (1969) Zbl0189.40603MR0259693
- J.-L. Lions E. Magenes, Problèrnes aux limites non homogènes et applications I, III, Dunod, Paris 1968. (1968)
- 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. (1973) MR0481401
- R. C. MacCamy V. C. Mizel, 10.1007/BF00250932, Arch. Rational Mech. Anal. 25 (1967), 299-320. (1967) MR0216165DOI10.1007/BF00250932
- E. J. McShane, Integration, Princeton University Press 1947. (1947) Zbl0033.05302MR0082536
- H. Pecher, 10.1016/0022-247X(80)90033-5, J. Math. Anal. Appl. 73 (1980), 278-299. (1980) Zbl0429.35057MR0560948DOI10.1016/0022-247X(80)90033-5
- M. A. Prestel, 10.1016/0362-546X(82)90089-X, Nonlinear Anal. 6 (1982), 209-216. (1982) Zbl0504.35065MR0654313DOI10.1016/0362-546X(82)90089-X
- C. O. A. Sowunmi, On the existence of periodic solutions of the equation , Rend. Ist. Mat. Univ. Trieste 8 (1976), 58-68. (1976) MR0430486
- I. Straškraba O. Vejvoda, Periodic solutions to abstract differential equations, Czechoslovak Math. J. 23 (1973), 635-669, 27 (1977), 511-513. (1973) MR0499577
- A. E. Taylor, Introduction to functional analysis, J. Wiley and Sons, Inc., New York 1958. (1958) Zbl0081.10202MR0098966
- M. Tsutsumi, Some nonlinear evolution equations of second order, Proc. Japan Acad. 47 (1971), 950-955. (1971) Zbl0258.35017MR0312023
- G. F. Webb, 10.4153/CJM-1980-049-5, Canad. J. Math. 32 (1980), 631-643. (1980) Zbl0414.35046MR0586981DOI10.4153/CJM-1980-049-5
- Y. Yamada, Note on certain nonlinear evolution equations of second order, Proc. Japan Acad. 55 (1979), 167-171. (1979) Zbl0436.47054MR0533540
- Y. Yamada, Some remarks on the equation , Osaka J. Math. 17 (1980), 303-323. (1980) MR0587752
- Y. Yamada, 10.1017/S0027763000019553, Nagoya Math. J. 84(1981), 31-83. (1981) Zbl0472.35052MR0641147DOI10.1017/S0027763000019553
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