메뉴 건너뛰기




Volumn 34, Issue 3, 1996, Pages 892-912

The Korteweg-de Vries equation on a periodic domain with singular-point dissipation

Author keywords

KdV equation; Point dissipation; Stabilization

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FEEDBACK; GREEN'S FUNCTION; NONLINEAR EQUATIONS; SYSTEM STABILITY;

EID: 0030150190     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012994269491     Document Type: Article
Times cited : (15)

References (16)
  • 1
    • 0001119719 scopus 로고
    • The initial value problem for the Korteweg-de Vries equation
    • J. L. BONA AND R. SMITH, The initial value problem for the Korteweg-de Vries equation, Proc. Roy. Soc. London Ser. A, 278 (1978), pp. 555-601.
    • (1978) Proc. Roy. Soc. London Ser. A , vol.278 , pp. 555-601
    • Bona, J.L.1    Smith, R.2
  • 2
    • 0009303159 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part II: The KdV equation
    • J. BOURGAIN, Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part II: the KdV equation, Geom. Funct. Analy., 3 (1993), pp. 209-262.
    • (1993) Geom. Funct. Analy. , vol.3 , pp. 209-262
    • Bourgain, J.1
  • 5
    • 84974004169 scopus 로고
    • The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
    • C. E. KENIG, G. PONCE, AND L. VEGA, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J., 71 (1993), pp. 1-21.
    • (1993) Duke Math. J. , vol.71 , pp. 1-21
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 6
    • 85033870561 scopus 로고
    • Private communications
    • V. KOMORNIK, Private communications, 1992.
    • (1992)
    • Komornik, V.1
  • 8
    • 85033844267 scopus 로고    scopus 로고
    • Control and stabilization of the Korteweg-de Vries equation on a periodic domain
    • to appear
    • _, Control and stabilization of the Korteweg-de Vries equation on a periodic domain, J. Differential Equations, to appear.
    • J. Differential Equations
  • 9
    • 0016973738 scopus 로고
    • The Korteweg-de Vries equation: A survey of results
    • R. M. MIURA, The Korteweg-de Vries equation: A survey of results. SIAM Rev., 18 (1976), pp. 412-459.
    • (1976) SIAM Rev. , vol.18 , pp. 412-459
    • Miura, R.M.1
  • 10
    • 0003316678 scopus 로고
    • Semigroup of Linear Operators and Applications to Partial Differential Equations
    • Springer-Verlag, New York
    • A. PAZY, Semigroup of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Springer-Verlag, New York, 1983.
    • (1983) Appl. Math. Sci. , vol.44
    • Pazy, A.1
  • 11
    • 0000820706 scopus 로고
    • Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions
    • D. L. RUSSELL, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), pp. 639-739.
    • (1978) SIAM Rev. , vol.20 , pp. 639-739
    • Russell, D.L.1
  • 12
    • 0027594486 scopus 로고
    • Controllability and stabilizability of the third order linear dispersion equation on a periodic domain
    • D. L. RUSSELL, AND B.-Y. ZHANG, Controllability and stabilizability of the third order linear dispersion equation on a periodic domain, SIAM J. Control Optim., 31 (1993), pp. 659-676.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 659-676
    • Russell, D.L.1    Zhang, B.-Y.2
  • 13
    • 0000140289 scopus 로고
    • Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation
    • _, Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation, J. Math. Anal. Appl., 190 (1995), pp. 449-488.
    • (1995) J. Math. Anal. Appl. , vol.190 , pp. 449-488
  • 15
    • 51649183085 scopus 로고
    • Remarks on the Korteweg-de Vries equation
    • J. C. SAUT AND R. TEMAN, Remarks on the Korteweg-de Vries equation, Israel J. Math., 24 (1976), pp. 78-87.
    • (1976) Israel J. Math. , vol.24 , pp. 78-87
    • Saut, J.C.1    Teman, R.2
  • 16
    • 0001022477 scopus 로고
    • Oscillatory integrals in Fourier analysis
    • E. M. Stein, ed., Princeton University Press, Princeton, NJ
    • E. M. STEIN, Oscillatory integrals in Fourier analysis, in Beijing Lectures in Harmonic Analysis, Ann. of Math. Stud. 112, E. M. Stein, ed., Princeton University Press, Princeton, NJ, 1986, pp. 307-355.
    • (1986) Beijing Lectures in Harmonic Analysis, Ann. of Math. Stud. , vol.112 , pp. 307-355
    • Stein, E.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.