메뉴 건너뛰기




Volumn 38, Issue 4, 1999, Pages 447-470

On the damped Boussinesq equation in a circle

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

EID: 0033229530     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00207-7     Document Type: Article
Times cited : (21)

References (43)
  • 1
    • 0002004721 scopus 로고
    • Solitons, Nonlinear Evolution Equations, and the Inverse Scattering
    • Cambridge Univ. Press, Cambridge
    • M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations, and the Inverse Scattering, Lond. Math. Soc., Cambridge Univ. Press, Cambridge, 1991.
    • (1991) Lond. Math. Soc.
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 3
    • 84963436255 scopus 로고
    • Regular decay of solutions of strongly damped nonlinear hyperbolic equations
    • P. Biler, Regular decay of solutions of strongly damped nonlinear hyperbolic equations, Appl. Anal. 32 (1989) 277-285.
    • (1989) Appl. Anal. , vol.32 , pp. 277-285
    • Biler, P.1
  • 4
    • 0009349901 scopus 로고
    • A singular perturbation problem for nonlinear damped hyperbolic equations
    • P. Biler, A singular perturbation problem for nonlinear damped hyperbolic equations, Proc. Roy. Soc. Edinburgh 111A (1989) 21-31.
    • (1989) Proc. Roy. Soc. Edinburgh , vol.111 A , pp. 21-31
    • Biler, P.1
  • 5
    • 84988189750 scopus 로고
    • Time decay of solutions of semilinear strongly damped generalized wave equations
    • P. Biler, Time decay of solutions of semilinear strongly damped generalized wave equations, Math. Meth. Appl. Sci. 14 (1991) 427-443.
    • (1991) Math. Meth. Appl. Sci. , vol.14 , pp. 427-443
    • Biler, P.1
  • 6
    • 0001068773 scopus 로고
    • More results on the decay of solutions to nonlinear, dispersive wave equations
    • J. Bona, L. Luo, More results on the decay of solutions to nonlinear, dispersive wave equations, Discrete Continuous Dyn. Systems 1 (2) (1995) 151-193.
    • (1995) Discrete Continuous Dyn. Systems , vol.1 , Issue.2 , pp. 151-193
    • Bona, J.1    Luo, L.2
  • 7
    • 34250086052 scopus 로고
    • Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
    • J. Bona, R. Sachs, Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation, Comm. Math. Phys. 118 (1988) 15-29.
    • (1988) Comm. Math. Phys. , vol.118 , pp. 15-29
    • Bona, J.1    Sachs, R.2
  • 8
    • 0001864672 scopus 로고
    • Theorie des ondes et de remous qui se propagent le long d'un canal rectangulaire horizontal
    • J. Boussinesq, Theorie des ondes et de remous qui se propagent le long d'un canal rectangulaire horizontal ..., J. Math. Pure Appl. Ser. 2 17 (1872) 55-108.
    • (1872) J. Math. Pure Appl. Ser. 2 , vol.17 , pp. 55-108
    • Boussinesq, J.1
  • 10
  • 11
    • 0003377886 scopus 로고
    • Nonlocal analogs of the nonlinear Boussinesq equation for surface waves over the rough bottom and their asymptotic solutions
    • in Russian
    • S.Yu. Dobrokhotov, Nonlocal analogs of the nonlinear Boussinesq equation for surface waves over the rough bottom and their asymptotic solutions, Dokl. Acad. Nauk SSSR 292 (1987) 63-67 (in Russian).
    • (1987) Dokl. Acad. Nauk SSSR , vol.292 , pp. 63-67
    • Dobrokhotov, S.Y.1
  • 12
    • 58149212439 scopus 로고
    • The structure of the rational solutions to the Boussinesq equation
    • V.M. Galkin, Pelinovsky, Yu.A. Stepanyants, The structure of the rational solutions to the Boussinesq equation, Physica D 80 (1995) 246-255.
    • (1995) Physica D , vol.80 , pp. 246-255
    • Galkin, V.M.1    Pelinovsky, Y.A.S.2
  • 13
    • 0009416148 scopus 로고
    • Solutions of the classical Boussinesq equation and the spherical Boussinesq equation: The Wronskian technique
    • R. Hirota, Solutions of the classical Boussinesq equation and the spherical Boussinesq equation: the Wronskian technique, J. Phys. Soc. Japan 55 (1986) 2137-2150.
    • (1986) J. Phys. Soc. Japan , vol.55 , pp. 2137-2150
    • Hirota, R.1
  • 14
    • 84972498136 scopus 로고
    • Uniform decay of weak solutions to a von Karman plate with nonlinear boundary dissipation
    • M.A. Horn, I. Lasiecka, Uniform decay of weak solutions to a von Karman plate with nonlinear boundary dissipation, Diff. Integral Eqns. 7 (4) (1994) 885-908.
    • (1994) Diff. Integral Eqns. , vol.7 , Issue.4 , pp. 885-908
    • Horn, M.A.1    Lasiecka, I.2
  • 16
    • 0002554581 scopus 로고
    • The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
    • V.K. Kalantarov, O.A. Ladyzhenskaya, The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types, J. Sov. Math. 10 (1978) 53-70.
    • (1978) J. Sov. Math. , vol.10 , pp. 53-70
    • Kalantarov, V.K.1    Ladyzhenskaya, O.A.2
  • 17
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. 39 (1895) 422-443.
    • (1895) Philos. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 18
    • 84972506618 scopus 로고
    • Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
    • I. Lasiecka, D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Diff. Integral Eqns. 6 (3) (1993) 507-533.
    • (1993) Diff. Integral Eqns. , vol.6 , Issue.3 , pp. 507-533
    • Lasiecka, I.1    Tataru, D.2
  • 21
    • 0000019045 scopus 로고
    • Global existence of small solutions for a generalized Boussinesq equation
    • F. Linares, Global existence of small solutions for a generalized Boussinesq equation, J. Diff. Eqs. 106 (1993) 257-293.
    • (1993) J. Diff. Eqs. , vol.106 , pp. 257-293
    • Linares, F.1
  • 22
    • 0009392123 scopus 로고
    • Asymptotic behavior of solutions of a generalized Boussinesq-type equation
    • F. Linares, M. Scialom, Asymptotic behavior of solutions of a generalized Boussinesq-type equation, Nonlinear Anal. 25 (1995) 1147-1158.
    • (1995) Nonlinear Anal. , vol.25 , pp. 1147-1158
    • Linares, F.1    Scialom, M.2
  • 24
    • 0009353016 scopus 로고
    • Solutions of the Boussinesq equation on a periodic domain
    • F.-L. Liu, D. Russell, Solutions of the Boussinesq equation on a periodic domain, J. Math. Anal. Appl. 192 (1995) 194-219.
    • (1995) J. Math. Anal. Appl. , vol.192 , pp. 194-219
    • Liu, F.-L.1    Russell, D.2
  • 25
    • 0001535009 scopus 로고
    • Soliton and anti-soliton interaction in the "good" Boussinesq equation
    • V.S. Manoranjan, T. Ortega, J.M. Sanz-Serna, Soliton and anti-soliton interaction in the "good" Boussinesq equation, J. Math. Phys. 29 (1988) 1964-1968.
    • (1988) J. Math. Phys. , vol.29 , pp. 1964-1968
    • Manoranjan, V.S.1    Ortega, T.2    Sanz-Serna, J.M.3
  • 28
    • 0003297871 scopus 로고
    • Nonlinear Nonlocal Equations in the Theory of Waves
    • AMS, Providence, RI
    • P.I. Naumkin, I.A. Shishmarev, Nonlinear Nonlocal Equations in the Theory of Waves, Transl. Math. Monographs, vol. 133, AMS, Providence, RI, 1994.
    • (1994) Transl. Math. Monographs , vol.133
    • Naumkin, P.I.1    Shishmarev, I.A.2
  • 31
    • 0000890754 scopus 로고
    • On the Cauchy problem for the Boussinesq-type equation
    • M. Tsutsumi, T. Matahashi, On the Cauchy problem for the Boussinesq-type equation, Math. Japonica 36 (2) (1991) 371-379.
    • (1991) Math. Japonica , vol.36 , Issue.2 , pp. 371-379
    • Tsutsumi, M.1    Matahashi, T.2
  • 32
    • 0009399407 scopus 로고
    • The asymptotic form for long times of the solution of the Boussinesq equation with dissipation
    • English transl. of the Russian journal
    • V.V. Varlamov, The asymptotic form for long times of the solution of the Boussinesq equation with dissipation, Comp. Maths Math. Phy. 34 (8/9) (1994) 1033-1043. English transl. of the Russian journal.
    • (1994) Comp. Maths Math. Phy. , vol.34 , Issue.8-9 , pp. 1033-1043
    • Varlamov, V.V.1
  • 33
    • 0000521880 scopus 로고    scopus 로고
    • On the Cauchy problem for the damped Boussinesq equation
    • V.V. Varlamov, On the Cauchy problem for the damped Boussinesq equation, Differential Integral Equations 9 (3) (1996) 619-634.
    • (1996) Differential Integral Equations , vol.9 , Issue.3 , pp. 619-634
    • Varlamov, V.V.1
  • 34
    • 0030150138 scopus 로고    scopus 로고
    • Existence and uniqueness of a solution to the Cauchy problem for the damped Boussinesq equation
    • V.V. Varlamov, Existence and uniqueness of a solution to the Cauchy problem for the damped Boussinesq equation, Math. Meth. Appl. Sci. 19 (1996) 639-649.
    • (1996) Math. Meth. Appl. Sci. , vol.19 , pp. 639-649
    • Varlamov, V.V.1
  • 35
    • 0040091802 scopus 로고    scopus 로고
    • On the third order nonlinear evolution equation governing wave propagation in relaxing media
    • V.V. Varlamov, On the third order nonlinear evolution equation governing wave propagation in relaxing media, Stud. Appl. Math. 99 (1997) 25-48.
    • (1997) Stud. Appl. Math. , vol.99 , pp. 25-48
    • Varlamov, V.V.1
  • 36
    • 0000107912 scopus 로고    scopus 로고
    • On spatially periodic solutions of the damped Boussinesq equation
    • V.V. Varlamov, On spatially periodic solutions of the damped Boussinesq equation, Diff. Integral Eqns. 10 (6) (1997) 1197-1211.
    • (1997) Diff. Integral Eqns. , vol.10 , Issue.6 , pp. 1197-1211
    • Varlamov, V.V.1
  • 37
    • 0032390266 scopus 로고    scopus 로고
    • On the initial-boundary value problem for the damped Boussinesq equation
    • V.V. Varlamov, On the initial-boundary value problem for the damped Boussinesq equation, Discrete Continuous Dyn. Systems 4 (3) (1998) 431-444.
    • (1998) Discrete Continuous Dyn. Systems , vol.4 , Issue.3 , pp. 431-444
    • Varlamov, V.V.1
  • 38
    • 3042999249 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
    • to appear
    • V.V. Varlamov, Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions, Int. J. Maths Math. Sci., to appear.
    • Int. J. Maths Math. Sci.
    • Varlamov, V.V.1
  • 39
    • 84990586440 scopus 로고
    • The Korteweg-de Vries equation with small dispersion: Higher order Lax-Levermore theory
    • S. Venakides, The Korteweg-de Vries equation with small dispersion: higher order Lax-Levermore theory, Comm. Pure Appl. Math. 43 (1990) 335-361.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 335-361
    • Venakides, S.1
  • 41
    • 0009446913 scopus 로고
    • On a growing mode of the Boussinesq equation
    • N. Yajima, On a growing mode of the Boussinesq equation, Progr. Theor. Phys. 69 (1983) 678-680.
    • (1983) Progr. Theor. Phys. , vol.69 , pp. 678-680
    • Yajima, N.1
  • 42
    • 0009345067 scopus 로고
    • Inertial manifolds and applications to nonlinear evolution equations
    • Trieste, Italy, May
    • Y. You, Inertial manifolds and applications to nonlinear evolution equations, ICTP Workshop, Trieste, Italy, May 1993, pp. 21-34.
    • (1993) ICTP Workshop , pp. 21-34
    • You, Y.1
  • 43
    • 0000060151 scopus 로고
    • On stochastization of one-dimensional chains of nonlinear oscillations
    • V.E. Zakharov, On stochastization of one-dimensional chains of nonlinear oscillations, Sov. Phys. JETP 38 (1974) 108-110.
    • (1974) Sov. Phys. JETP , vol.38 , pp. 108-110
    • Zakharov, V.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.