메뉴 건너뛰기




Volumn 204, Issue 3, 1996, Pages 729-753

On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030589799     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0464     Document Type: Article
Times cited : (107)

References (24)
  • 2
    • 0001709423 scopus 로고
    • The damped elastic stretched string equation generalized: Existence, uniqueness, regularity and stability
    • 2. E. H. Brito, The damped elastic stretched string equation generalized: existence, uniqueness, regularity and stability, Appl. Anal. 13 (1982), 219-233.
    • (1982) Appl. Anal. , vol.13 , pp. 219-233
    • Brito, E.H.1
  • 3
    • 0000028946 scopus 로고
    • Existence of a solution of the wave equation with nonlinear damping and source terms
    • 3. V. Georgiev and G. Todorova, Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differential Equations 109 (1994), 295-308.
    • (1994) J. Differential Equations , vol.109 , pp. 295-308
    • Georgiev, V.1    Todorova, G.2
  • 5
    • 0001142650 scopus 로고
    • On some nonlinear wave equations. II. Global existence and energy decay of solutions
    • 5. M. Hosoya and Y. Yamada, On some nonlinear wave equations. II. Global existence and energy decay of solutions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 38 (1991), 239-250.
    • (1991) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.38 , pp. 239-250
    • Hosoya, M.1    Yamada, Y.2
  • 6
    • 84972528316 scopus 로고
    • A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms
    • 6. R. Ikehata, A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms, Differential Integral Equations 8 (1995), 607-616.
    • (1995) Differential Integral Equations , vol.8 , pp. 607-616
    • Ikehata, R.1
  • 7
    • 0030296142 scopus 로고    scopus 로고
    • Some remarks on the wave equations with nonlinear damping and source terms
    • 7. R. Ikehata, Some remarks on the wave equations with nonlinear damping and source terms, Nonlinear Anal. 27 (1996), 1165-1175.
    • (1996) Nonlinear Anal. , vol.27 , pp. 1165-1175
    • Ikehata, R.1
  • 8
    • 0000311678 scopus 로고
    • A class of second order quasilinear evolution equations
    • 8. R. Ikehata and N. Okazawa, A class of second order quasilinear evolution equations, J. Differential Equations 114 (1994), 106-131.
    • (1994) J. Differential Equations , vol.114 , pp. 106-131
    • Ikehata, R.1    Okazawa, N.2
  • 9
    • 0000336342 scopus 로고
    • Asymptotic stability and blowing-up solutions of some nonlinear equations
    • 9. H. Ishii, Asymptotic stability and blowing-up solutions of some nonlinear equations, J. Differential Equations 26 (1977), 291-319.
    • (1977) J. Differential Equations , vol.26 , pp. 291-319
    • Ishii, H.1
  • 13
    • 85029970919 scopus 로고    scopus 로고
    • Energy decay for the wave equations of Kirchhoff type with linear damping terms
    • in press
    • 13. T. Matsuyama and R. Ikehata, Energy decay for the wave equations of Kirchhoff type with linear damping terms, Math. Japon., in press.
    • Math. Japon.
    • Matsuyama, T.1    Ikehata, R.2
  • 14
    • 0000473871 scopus 로고
    • Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state
    • 14. M. Nakao, Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state, Mem. Fac. Sci. Kyushu Univ. 30 (1976), 257-265.
    • (1976) Mem. Fac. Sci. Kyushu Univ. , vol.30 , pp. 257-265
    • Nakao, M.1
  • 15
    • 0000907825 scopus 로고
    • Asymptotic stability of the bounded or almost periodic solutions of the wave equation with nonlinear dissipative term
    • 15. M. Nakao, Asymptotic stability of the bounded or almost periodic solutions of the wave equation with nonlinear dissipative term, J. Math. Anal. Appl. 58 (1977), 336-343.
    • (1977) J. Math. Anal. Appl. , vol.58 , pp. 336-343
    • Nakao, M.1
  • 16
    • 0000632070 scopus 로고
    • Global existence of classical solutions to the initial-boundary value problem of the semilinear wave equations with a degenerate dissipative term
    • 16. M. Nakao, Global existence of classical solutions to the initial-boundary value problem of the semilinear wave equations with a degenerate dissipative term, Nonlinear Anal. 15 (1990), 115-140.
    • (1990) Nonlinear Anal. , vol.15 , pp. 115-140
    • Nakao, M.1
  • 17
    • 51249177315 scopus 로고
    • Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations
    • 17. M. Nakao, Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations, Math. Z. 206 (1991), 265-276.
    • (1991) Math. Z. , vol.206 , pp. 265-276
    • Nakao, M.1
  • 18
    • 0000901772 scopus 로고
    • Existence of global smooth solutions to the initial-boundary value problem for the quasilinear hyperbolic equation with a degenerate dissipative term
    • 18. M. Nakao, Existence of global smooth solutions to the initial-boundary value problem for the quasilinear hyperbolic equation with a degenerate dissipative term, J. Differential Equations 98 (1992), 299-327.
    • (1992) J. Differential Equations , vol.98 , pp. 299-327
    • Nakao, M.1
  • 19
    • 0000313909 scopus 로고
    • Global existence to the Cauchy problem of the semilinear wave equation with a nonlinear dissipation
    • 19. M. Nakao and K. Ono, Global existence to the Cauchy problem of the semilinear wave equation with a nonlinear dissipation, Funkcial. Ekvac. 38 (1995), 417-431.
    • (1995) Funkcial. Ekvac. , vol.38 , pp. 417-431
    • Nakao, M.1    Ono, K.2
  • 20
    • 0000764253 scopus 로고
    • Exponential decay of solutions of some quasilinear hyperbolic equations with linear damping
    • 20. K. Nishihara, Exponential decay of solutions of some quasilinear hyperbolic equations with linear damping, Nonlinear Anal. 8 (1984), 623-636.
    • (1984) Nonlinear Anal. , vol.8 , pp. 623-636
    • Nishihara, K.1
  • 21
    • 51649189214 scopus 로고
    • Saddle points and unstability of nonlinear hyperbolic equations
    • 21. L. E. Payne and D. H. Sattinger, Saddle points and unstability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303.
    • (1975) Israel J. Math. , vol.22 , pp. 273-303
    • Payne, L.E.1    Sattinger, D.H.2
  • 22
    • 0000886834 scopus 로고
    • On global solution of nonlinear hyperbolic equations
    • 22. D. H. Sattinger, On global solution of nonlinear hyperbolic equations, Arch. Rational Mech. Anal. 30 (1968), 148-172.
    • (1968) Arch. Rational Mech. Anal. , vol.30 , pp. 148-172
    • Sattinger, D.H.1
  • 23
    • 0000877229 scopus 로고
    • On solutions of semilinear differential equations in a Hilbert space
    • 23. M. Tsutsumi, On solutions of semilinear differential equations in a Hilbert space, Math. Japon. 17 (1972), 173-193.
    • (1972) Math. Japon. , vol.17 , pp. 173-193
    • Tsutsumi, M.1
  • 24
    • 84972536297 scopus 로고
    • On some quasilinear wave equations with dissipative terms
    • 24. Y. Yamada, On some quasilinear wave equations with dissipative terms, Nagoya Math. J. 187 (1982), 17-39.
    • (1982) Nagoya Math. J. , vol.187 , pp. 17-39
    • Yamada, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.