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In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.
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참고문헌 (24)
참고문헌 신청
A. Constantin / 2002 / The initial value problem for a generalized Boussinesq equation / Differential Integral Equations 15(9):1061~1072
G. B. Folland / 1999 / Real Analysis, second edition, Pure and Applied Mathematics (New York) / John Wiley & Sons, Inc.
T. Kato / 1988 / Commutator estimates and the Euler and Navier-Stokes equations / Comm. Pure Appl. Math. 41(7):891~907
N. Kutev / 2013 / Global existence of Cauchy problem for Boussinesq paradigm equation / Comput. Math. Appl. 65(3):500~511
S. Lai / 2003 / The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation / Discrete Contin. Dyn. Syst. Ser. B 3(3):401~408
G. B. Folland / 1999 / Real Analysis, second edition, Pure and Applied Mathematics (New York) / John Wiley & Sons, Inc.
T. Kato / 1988 / Commutator estimates and the Euler and Navier-Stokes equations / Comm. Pure Appl. Math. 41(7):891~907
N. Kutev / 2013 / Global existence of Cauchy problem for Boussinesq paradigm equation / Comput. Math. Appl. 65(3):500~511
S. Lai / 2003 / The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation / Discrete Contin. Dyn. Syst. Ser. B 3(3):401~408
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