Initial boundary value problem of the generalized cubic double dispersion equation

Abstract

In this paper, the existence and the uniqueness of the global generalized solution and the global classical solution for the initial boundary value problem of the generalized cubic double dispersion equation are proved. The nonexistence of global solution for the initial boundary value problem of the generalized cubic double dispersion equation is discussed.

Lie Symmetry Reductions and Exact Solutions of a Multidimensional Double Dispersion Equation

“…In [12] [13], Chen and Wang studied the initial-boundary value problem and the Cauchy problem of the following generalized double dispersion equation which includes above Equation ( Recently in [14], the authors considered the Cauchy problem of the multidimensional nonlinear evolution equation…”

Global attractor for the generalized double dispersion equation

“…(1.1) includes (1.5) as its special case. There have been lots of research studies on the well-posedness, blowup, asymptotic behavior and other properties of solutions for both the IBVP and the IVP of the equation of type (1.1) (see [1,5,6,8,9,[22][23][24][25][26][30][31][32][33] and references therein). While for the investigation on the global attractor to Eq.…”

Exact solutions of a generalized Boussinesq equation

“…This equation was studied in [3], [4]. The initial boundary value problem and the Cauchy problem of a generalized double dispersion equation, which includes (3) as a special case, were studied in [5]- [8]. Symmetry reductions and exact solutions have several different important applications in the context of differential equations.…”