A non-homogeneous boundary-value problem for the Korteweg–de Vries equation posed on a finite domain II
暂无分享,去创建一个
[1] L. R. Scott,et al. An evaluation of a model equation for water waves , 1981, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[2] J. Bona,et al. Model equations for long waves in nonlinear dispersive systems , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[3] Roger Temam,et al. Remarks on the Korteweg-de Vries equation , 1976 .
[4] Daniel B. Dix. Nonuniqueness and uniqueness in the initial-value problem for Burgers' equation , 1996 .
[5] Luis Vega,et al. The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices , 1993 .
[6] A. Faminskii. Mixed problems for the Korteweg-de Vries equation , 1999 .
[7] Bing-Yu Zhang,et al. A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane , 2001 .
[8] H. Segur,et al. The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments , 1974, Journal of Fluid Mechanics.
[9] Luis Vega. Schrödinger equations: pointwise convergence to the initial data , 1988 .
[10] J. Hammack. A note on tsunamis: their generation and propagation in an ocean of uniform depth , 1973, Journal of Fluid Mechanics.
[11] S. Sun,et al. The Korteweg--de Vries Equation on a Periodic Domain with Singular-Point Dissipation , 1996 .
[12] Ragnar Winther,et al. The Korteweg–de Vries Equation, Posed in a Quarter-Plane , 1983 .
[13] Jerry L. Bona,et al. A mathematical model for long waves generated by wavemakers in non-linear dispersive systems , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.
[14] Jerry L. Bona,et al. An initial- and boundary-value problem for a model equation for propagation of long waves , 1980 .
[15] Peter Constantin,et al. Local smoothing properties of dispersive equations , 1988 .
[16] E. Davies,et al. SEMIGROUPS OF LINEAR OPERATORS AND APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS: (Applied Mathematical Sciences, 44) , 1984 .
[17] 乔花玲,et al. 关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解 , 2003 .
[18] Luis Vega,et al. A bilinear estimate with applications to the KdV equation , 1996 .
[19] C. S. Gardner,et al. Korteweg-devries equation and generalizations. VI. methods for exact solution , 1974 .
[20] J. Bourgain,et al. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations , 1993 .
[21] Jerry L. Bona,et al. Solutions of the Korteweg-de Vries equation in frac-tional order Sobolev space , 1976 .
[22] P. Lax. INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES. , 1968 .
[23] W. D. Evans,et al. PARTIAL DIFFERENTIAL EQUATIONS , 1941 .
[24] Bing-Yu Zhang,et al. A remark on the Cauchy problem for the Korteweg-de Vries equation on a periodic domain , 1995, Differential and Integral Equations.
[25] Luis Vega,et al. Well-posedness of the initial value problem for the Korteweg-de Vries equation , 1991 .
[26] W. Strauss,et al. Gain of regularity for equations of KdV type , 1992 .
[27] N. J. Zabusky,et al. Shallow-water waves, the Korteweg-deVries equation and solitons , 1971, Journal of Fluid Mechanics.
[28] J. Bona,et al. The Korteweg-de Vries equation in a quarter plane, continuous dependence results , 1989, Differential and Integral Equations.
[29] Terence Tao,et al. Sharp global well-posedness for KdV and modified KdV on ℝ and , 2003 .
[30] Bing-Yu Zhang,et al. Taylor Series Expansion for Solutions of the Korteweg-deVries Equation with Respect to Their Initial Values , 1995 .
[31] Bing-Yu Zhang,et al. Analyticity of solutions of the generalized Korteweg-De Vries equation with respect to their initial values , 1995 .
[32] Bing-Yu Zhang,et al. Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation , 2012, Acta Applicandae Mathematicae.
[33] A. Sjöberg. On the Korteweg-de Vries equation: Existence and uniqueness , 1970 .
[34] Bing-Yu Zhang,et al. Exact Boundary Controllability of the Korteweg--de Vries Equation , 1999 .
[35] Bing-Yu Zhang,et al. A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain , 2003 .
[36] D. Korteweg,et al. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .
[37] W. Rudin. Real and complex analysis , 1968 .
[38] Luis Vega,et al. Oscillatory integrals and regularity of dispersive equations , 1991 .
[39] Luc Molinet,et al. On the Cauchy Problem for the Generalized Korteweg-de Vries Equation , 2003 .
[40] Shu-Ming Sun,et al. Conditional and unconditional well-posedness for nonlinear evolution equations , 2004 .
[41] J. Bona,et al. The initial-value problem for the Korteweg-de Vries equation , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[42] Gert Eilenberger,et al. The Korteweg-de Vries Equation (KdV-Equation) , 1981 .
[43] Lionel Rosier,et al. Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain , 1997 .
[44] Jerry L. Bona,et al. Interaction of internal waves with the seabed on continental shelves , 1991 .
[45] C. Kenig,et al. Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle , 1993 .
[46] C. Eugene Wayne,et al. Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory , 1990 .
[47] H. Takaoka,et al. Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$ , 2001 .
[48] Tosio Kato,et al. On the Korteweg-de Vries equation , 1979 .
[49] Shu-Ming Sun,et al. Forced Oscillations of a Damped Korteweg-de Vries Equation in a Quarter Plane , 2003 .
[50] L. Tartar. Interpolation non linéaire et régularité , 1972 .
[51] Jean-Michel Ghidaglia,et al. An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval , 2001, Advances in Differential Equations.
[52] J. E. Colliander,et al. THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE , 2001 .
[53] Justin Holmer. The Initial-Boundary Value Problem for the Korteweg–de Vries Equation , 2005 .
[54] Francis Ribaud,et al. On the low regularity of the Korteweg-de Vries-Burgers equation , 2002 .
[55] D. Russell. Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .
[56] David L. Russell,et al. Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain , 1993 .
[57] David L. Russell,et al. Exact controllability and stabilizability of the Korteweg-de Vries equation , 1996 .
[58] A. Faminskii. An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces , 2005 .
[59] R. Miura. The Korteweg–deVries Equation: A Survey of Results , 1976 .
[60] David L. Russell,et al. Smoothing and Decay Properties of Solutions of the Korteweg-deVries Equation on a Periodic Domain with Point Dissipation , 1995 .