메뉴 건너뛰기




Volumn 22, Issue 1, 2003, Pages 167-177

Exponential growth for a fractionally damped wave equation

Author keywords

Exponential growth; Fractional derivative; Internal damping

Indexed keywords


EID: 0037229854     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/zaa/1137     Document Type: Article
Times cited : (35)

References (36)
  • 3
    • 85157089949 scopus 로고    scopus 로고
    • On the asymptotic behavior of semilinear wave equations with degenerate dissipation and source terms
    • Georgiev, V. and A. Milani: On the asymptotic behavior of semilinear wave equations with degenerate dissipation and source terms. Trieste: Intern. Centre Theor. Phys. IC/96/96 (1996).
    • (1996) Trieste: Intern. Centre Theor. Phys. , vol.IC-96-96
    • Georgiev, V.1    Milani, A.2
  • 4
    • 0000775998 scopus 로고
    • Blow up theorems for nonlinear wave equations
    • Glassey, R. T.: Blow up theorems for nonlinear wave equations. Math. Z. 132 (1973), 183 - 203.
    • (1973) Math. Z. , vol.132 , pp. 183-203
    • Glassey, R.T.1
  • 5
    • 0000775450 scopus 로고
    • Finite time blow up for solutions of nonlinear wave equations
    • Glassey, R. T.: Finite time blow up for solutions of nonlinear wave equations. Math. Z. 177 (1981), 323 - 340.
    • (1981) Math. Z. , vol.177 , pp. 323-340
    • Glassey, R.T.1
  • 6
    • 0000337016 scopus 로고
    • Existence in the large for u = F(u) in two space dimensions
    • Glassey, R. T.: Existence in the large for u = F(u) in two space dimensions. Mat. Z. 178 (1981), 233 - 261.
    • (1981) Mat. Z. , vol.178 , pp. 233-261
    • Glassey, R.T.1
  • 9
    • 85157105084 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions to a diffusive Volterra equation
    • Guedda, M., Kirane, M. and N.-e. Tatar: Asymptotic behavior of solutions to a diffusive Volterra equation. Comm. Appl. Anal. 1 (1997), 91 - 102.
    • (1997) Comm. Appl. Anal. , vol.1 , pp. 91-102
    • Guedda, M.1    Kirane, M.2    Tatar, N.-E.3
  • 10
    • 0012421053 scopus 로고
    • A two weights inequality for the fractional integral when p = n/α
    • Harboure, E., Macias, R. A. and C. Segovia: A two weights inequality for the fractional integral when p = n/α. Proc. Amer. Math. Soc. 90 (1984), 555 - 562.
    • (1984) Proc. Amer. Math. Soc. , vol.90 , pp. 555-562
    • Harboure, E.1    Macias, R.A.2    Segovia, C.3
  • 12
    • 0001425550 scopus 로고    scopus 로고
    • Stable and unstable sets for evolution equations of parabolic and hyperbolic type
    • Ikehata, R. and T. Suzuki: Stable and unstable sets for evolution equations of parabolic and hyperbolic type. Hiroshima Math. J. 26 (1996), 475 - 491.
    • (1996) Hiroshima Math. J. , vol.26 , pp. 475-491
    • Ikehata, R.1    Suzuki, T.2
  • 13
    • 0000774996 scopus 로고
    • Blow up of solutions of nonlinear wave equations in three space dimensions
    • John, F.: Blow up of solutions of nonlinear wave equations in three space dimensions. Manuscripta Mat. 28 (1979), 235 - 268.
    • (1979) Manuscripta Mat. , vol.28 , pp. 235-268
    • John, F.1
  • 14
    • 84980081022 scopus 로고
    • On solutions of nonlinear wave equations
    • Keller, J.: On solutions of nonlinear wave equations. Comm. Pure Appl. Math. 10 (1957), 523 - 532.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 523-532
    • Keller, J.1
  • 15
    • 0012415112 scopus 로고    scopus 로고
    • Existence and uniqueness theorem for nonlinear fractional differential equations
    • Kilbas, A. A., Bonilla, B. and J. J. Trujillo: Existence and uniqueness theorem for nonlinear fractional differential equations. Dem. Math. 33 (2000), 583 - 602.
    • (2000) Dem. Math. , vol.33 , pp. 583-602
    • Kilbas, A.A.1    Bonilla, B.2    Trujillo, J.J.3
  • 16
    • 0012378240 scopus 로고    scopus 로고
    • A memory type boundary stabilization of a mildly damped wave equation
    • Kirane, M. and N.-e. Tatar: A memory type boundary stabilization of a mildly damped wave equation. Electr. J. Qual. Theory Diff. Eqs. (1999)6, 1 - 7.
    • (1999) Electr. J. Qual. Theory Diff. Eqs. , Issue.6 , pp. 1-7
    • Kirane, M.1    Tatar, N.-E.2
  • 17
    • 23044518140 scopus 로고    scopus 로고
    • Non-existence results for a semilinear hyperbolic problem with boundary condition of memory type
    • Kirane, M. and N.-e. Tatar: Non-existence results for a semilinear hyperbolic problem with boundary condition of memory type. Z. Anal. Anw. 19 (2000), 453 - 468.
    • (2000) Z. Anal. Anw. , vol.19 , pp. 453-468
    • Kirane, M.1    Tatar, N.-E.2
  • 18
    • 85157287613 scopus 로고    scopus 로고
    • Asymptotic stability and blow up for a fractional differential equation
    • Kirane, M. and N.-e. Tatar: Asymptotic stability and blow up for a fractional differential equation. Submitted to FCAA.
    • FCAA
    • Kirane, M.1    Tatar, N.-E.2
  • 20
    • 0012474708 scopus 로고
    • Wave equation with singular delqayed time
    • Lokshin, A. A.: Wave equation with singular delqayed time (in Russian). Dokl. Akad. Nauk. SSSR 240 (1978), 43 - 46.
    • (1978) Dokl. Akad. Nauk. SSSR , vol.240 , pp. 43-46
    • Lokshin, A.A.1
  • 21
    • 0000911022 scopus 로고
    • Fundamental solutions of the wave equation with delayed time
    • Lokshin, A. A. and V. E. Rok: Fundamental solutions of the wave equation with delayed time (in Russian). Dokl. Akad. Nauk. SSSR 239 (1978), 1305 - 1308.
    • (1978) Dokl. Akad. Nauk. SSSR , vol.239 , pp. 1305-1308
    • Lokshin, A.A.1    Rok, V.E.2
  • 23
    • 0000631041 scopus 로고
    • Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with first-order dissipation
    • Matsumura, A.: Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with first-order dissipation. Publ. Res. Inst. Sci. Kyoto Univ. 13 (1977), 349 - 379.
    • (1977) Publ. Res. Inst. Sci. Kyoto Univ. , vol.13 , pp. 349-379
    • Matsumura, A.1
  • 26
    • 0000313909 scopus 로고
    • Global existence to the Cauchy problem of the semilinear wave equation with a nonlinear dissipation
    • Nakao, M. and K. Ono: Global existence to the Cauchy problem of the semilinear wave equation with a nonlinear dissipation. Funkcialaj Ekvacioj 38 (1995) 417 - 431.
    • (1995) Funkcialaj Ekvacioj , vol.38 , pp. 417-431
    • Nakao, M.1    Ono, K.2
  • 27
    • 0000683386 scopus 로고
    • Frequency domain methods for Volterra equations
    • Nohel, J. A. and D. F. Shea: Frequency domain methods for Volterra equations. Adv. Math. 22 (1976), 278 - 304.
    • (1976) Adv. Math. , vol.22 , pp. 278-304
    • Nohel, J.A.1    Shea, D.F.2
  • 29
    • 51649189214 scopus 로고
    • Saddle points and unstability of nonlinear hyperbolic equations
    • Payne, L. E. 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
  • 30
    • 0003797958 scopus 로고    scopus 로고
    • Fractional differential equations
    • New York - London: Acad. Press
    • Podlubny, I.: Fractional Differential Equations (Math, in Sci. and Eng.: Vol. 198). New York - London: Acad. Press 1999.
    • (1999) Math, in Sci. and Eng. , vol.198
    • Podlubny, I.1
  • 31
    • 0000418185 scopus 로고    scopus 로고
    • Global non existence for abstract evolution equations with positive initial energy
    • Pucci, P. and J. Serrin: Global non existence for abstract evolution equations with positive initial energy. J. Diff. Eqs. 150 (1998), 203 - 214.
    • (1998) J. Diff. Eqs. , vol.150 , pp. 203-214
    • Pucci, P.1    Serrin, J.2
  • 33
    • 0000886834 scopus 로고
    • On global solution of nonlinear hyperbolic equations
    • Sattinger, D. H.: On global solution of nonlinear hyperbolic equations. Arch. Rat. Mech. Anal. 30 (1968), 148 - 172.
    • (1968) Arch. Rat. Mech. Anal. , vol.30 , pp. 148-172
    • Sattinger, D.H.1
  • 34
    • 0000546412 scopus 로고
    • Nonexistence of global solutions to semilinear wave equations in high dimensions
    • Sideris, T. C.: Nonexistence of global solutions to semilinear wave equations in high dimensions. J. Diff. Eqs. 52 (1984), 378 - 406.
    • (1984) J. Diff. Eqs. , vol.52 , pp. 378-406
    • Sideris, T.C.1
  • 35
    • 0000877229 scopus 로고
    • On solutions of semilinear differential equations in a Hilbert space
    • Tsutsumi, M.: 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.