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Volumn 50, Issue 4, 2001, Pages 1745-1775

The Cauchy problem for dissipative Korteweg De Vries equations in Sobolev spaces of negative order

(2)  Molinet, Luc a   Ribaud, Francis a  

a NONE

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EID: 0005360710     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2001.50.2135     Document Type: Article
Times cited : (47)

References (18)
  • 1
    • 0000823596 scopus 로고    scopus 로고
    • The initial-value problem for the generalized Burgers' equation
    • D. BEKIRANOV, The initial-value problem for the generalized Burgers' equation, Diff. Int. Eq. 9 (1996), 1253-1265.
    • (1996) Diff. Int. Eq. , vol.9 , pp. 1253-1265
    • Bekiranov, D.1
  • 2
    • 0001767796 scopus 로고
    • Decay of solutions to nonlinear, dispersive wave equations
    • J.L. BONA & L. LUO, Decay of solutions to nonlinear, dispersive wave equations, Philos. Trans. Royal Soc. London A 302 (1981), 457-510.
    • (1981) Philos. Trans. Royal Soc. London A , vol.302 , pp. 457-510
    • Bona, J.L.1    Lou, L.2
  • 3
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations
    • J. BOURGAIN, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations, GAFA, 3 (1993), 107-156.
    • (1993) GAFA , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 4
    • 0009303159 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations II. The KdV equation
    • _, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations II. The KdV equation, GAFA, 3 (1993), 209-262.
    • (1993) GAFA , vol.3 , pp. 209-262
  • 5
    • 0000044382 scopus 로고
    • Periodic Korteveg de Vries equation with measures as initial data
    • _, Periodic Korteveg de Vries equation with measures as initial data, Sci. Math. New. Ser. 3 (1993), 115-159.
    • (1993) Sci. Math. New. Ser. , vol.3 , pp. 115-159
  • 7
    • 0030537418 scopus 로고    scopus 로고
    • Nonuniqusness and uniqueness in the initial-value problem for Burger's equation
    • D. B. DIX, Nonuniqusness and uniqueness in the initial-value problem for Burger's equation, SIAM J. Math. Anal. 27 (1996), 708-724.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 708-724
    • Dix, D.B.1
  • 8
    • 0000575157 scopus 로고
    • The dissipation of nonlinear dispersive waves: Case of asymptotically weak nonlinearity
    • _, The dissipation of nonlinear dispersive waves: case of asymptotically weak nonlinearity, Comm. P.D.E. 17 (1992), 1665-1693.
    • (1992) Comm. P.D.E. , vol.17 , pp. 1665-1693
  • 9
    • 33747492074 scopus 로고
    • Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain),
    • J. GINIBRE, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain), In: Séminaire Bourbaki 796, Astérisque 237, 1995, 163-187.
    • (1995) Séminaire Bourbaki 796, Astérisque , vol.237 , pp. 163-187
    • Ginibre, J.1
  • 10
    • 58149363006 scopus 로고
    • On the Cauchy problem for the Zakharov system
    • J. GINIBRE, Y. TSUTSUMI & G. VELO, On the Cauchy problem for the Zakharov system, J. Funct. Analysis 133 (1995), 50-68.
    • (1995) J. Funct. Analysis , vol.133 , pp. 50-68
    • Ginibre, J.1    Tsutsumi, Y.2    Velo, G.3
  • 11
    • 0016532331 scopus 로고
    • Effect of viscosity on long gravity waves
    • T. KAKUTANI & K. MATSUUCHI, Effect of viscosity on long gravity waves, J. Phys. Soc. Japan, 39 (1975), 237-246.
    • (1975) J. Phys. Soc. Japan , vol.39 , pp. 237-246
    • Kakutani, T.1    Matsuuchi, K.2
  • 12
    • 84974004169 scopus 로고
    • The Cauchy problem for the Korteweg de Vries equation in Sobolev spaces of negative order
    • C. E. KENIG, G. PONCE & L. VEGA, The Cauchy problem for the Korteweg de Vries equation in Sobolev spaces of negative order, Duke Math. J. 71 (1993), 1-20.
    • (1993) Duke Math. J. , vol.71 , pp. 1-20
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 13
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to the KdV equation
    • C. E. KENIG, G. PONCE & L. VEGA, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9(2) (1996), 573-603.
    • (1996) J. Amer. Math. Soc. , vol.9 , Issue.2 , pp. 573-603
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 14
    • 0001442617 scopus 로고    scopus 로고
    • On the ill-posedness of some canonical dispersive equations
    • _, On the ill-posedness of some canonical dispersive equations, Duke Math J. 106 (2001), 617-633.
    • (2001) Duke Math J. , vol.106 , pp. 617-633
  • 15
    • 0000946209 scopus 로고
    • Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data
    • H. KOZONO & M. YAMAZAKI, Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Comm. P.D.E., 19 (5/6) (1994), 959-1014.
    • (1994) Comm. P.D.E. , vol.19 , Issue.5-6 , pp. 959-1014
    • Kozono, H.1    Yamazaki, M.2
  • 16
    • 84875108642 scopus 로고    scopus 로고
    • The global Cauchy problem in Bourgain's type spaces for a dispersive dissipative semilinear equation
    • to appear
    • L. MOLINET & F. RIBAUD, The global Cauchy problem in Bourgain's type spaces for a dispersive dissipative semilinear equation, SIAM J. Math. Anal. (to appear).
    • SIAM J. Math. Anal.
    • Molinet, L.1    Ribaud, F.2
  • 17
    • 0040470906 scopus 로고
    • Damping of solitary waves
    • E. OTT & N. SUDAN, Damping of solitary waves, Phys. Fluids, 13(6) (1970), 1432-1434.
    • (1970) Phys. Fluids , vol.13 , Issue.6 , pp. 1432-1434
    • Ott, E.1    Sudan, N.2
  • 18
    • 0031492827 scopus 로고    scopus 로고
    • Semilinear parabolic equations with distributions as initial data
    • F. RIBAUD, Semilinear Parabolic Equations with distributions as initial data, Disc. Cont. Dyn. Syst. 3 (1997), 305-316.
    • (1997) Disc. Cont. Dyn. Syst. , vol.3 , pp. 305-316
    • Ribaud, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.