본문 바로가기
KERD
논문KCI 등재

The initial-boundary-value problem of a generalized Boussinesq equation on the half line

Ruying Xue
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회지 (Journal of the KMS)|제45권 제1호|pp. 79-95

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

existenceBoussinesq equationinitial-boundary-value problem
주제분류수학

초록

The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing the Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation

Abstract

The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing the Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation

참고문헌 (12)

  1. J. L. Bona, "Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media II: The nonlinear theory", Nonlinearity, 17(3), pp.925~952 (2004)
  2. J. L. Bona, "Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation", Communications in Mathematical Physics, 118(1), pp.15~29 (1988)
  3. J. L. Bona, "A non-homogenous boundary-value problem for the Korteweg-de-Varies equation in a quarter plane", Transactions of the American Mathematical Society, 326, pp.427~490 (2001)
  4. J. E. Colliander, "The generalized Korteweg-de Vries equation on the half line", Communications in Partial Differential Equations, 27(11), pp.2187~2266 (2002)
  5. J. Holmer, "The initial-boundary value problem for the Korteweg-de Vries equation", Communications in Partial Differential Equations, 31(8), pp.1151~1190 (2006)
  6. C. E. Kenig, "Oscillatory integrals and regularity of dispersive equations", Indiana University Mathematics Journal, 40(1), pp.33~69 (1991)
  7. C. E. Kenig, "Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle", Communications On Pure & Applied Mathematics, 46(4), pp.527~620 (1993)
  8. F. Linares, "Global existence of small solutions for a generalized Boussinesq equation", Journal of Differential Equations, 106(2), pp.257~293 (1993)
  9. L. Molinet, "On the Cauchy problem for the generalized Korteweg-de Vries equation", Communications in Partial Differential Equations, 28(11), pp.2065~2091 (2003)
  10. A. K. Pani, "Finite element Galerkin method for the “good” Boussinesq equation", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 29(8), pp.937~956 (1997)
  11. V. Varlamov, "Long-time asymptotics for the damped Boussinesq equation in a disk, Electron", Journal of Differential Equations Conference, pp.285~298 (2000)
  12. R. Xue, "Local and global existence of solutions for the Cauchy problem of a generalized Boussinesq equation", Journal of Mathematical Analysis and Applications, 316(1), pp.307~327 (2006)

관련 논문AI추천

Global Small Solutions of the Cauchy Problem for NonisotropicSchodinger EquationsShangbin Cui, Xiangqing Zhao경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호Global existence and stability of a Korteweg-de Vries equation in noncylindrical domainTae Gab Ha대한수학회 · 대한수학회논문집2019 · 제34권 제2호Global well-posedness for the coupled system of Schr\"odinger and Kawahara equations신왕석대한수학회 · 대한수학회보2025 · 제62권 제6호Remarks on nonlinear Dirac equations in one space dimension허형진대한수학회 · 대한수학회논문집2015 · 제30권 제3호The Cauchy problem for an integrable generalized Camassa-Holm equation with cubic nonlinearityBin Liu, Lei Zhang대한수학회 · 대한수학회보2018 · 제55권 제1호Existence of strong mild solution of the Navier-Stokes equations in the half space with nondecaying initial data배형옥, 진범자대한수학회 · 대한수학회지2012 · 제49권 제1호

이 간행물의 다른 논문 (17건)

Elements of the KKM theory on abstract convex spaces박세희pp. 1-27Strong convergence for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappingsXiaolong Qin, Meijuan Shang, Yongfu Supp. 29-40Lorentzian surfaces with constant curvatures and transformations in the 3-dimensional Lorentzian space박준상pp. 41-61Holomorphic functions on the mixed norm spaces on the polydiscStevo Stevicpp. 63-78Integral representations in electrical impedance tomography using boundary integral operators권기운pp. 97-119
원문 보기