Existence, global nonexistence, and asymptotic behavior of solutionsfor the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation

Abstract

We consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.

Continuous dependence of solutions for damped improved Boussinesq equation

“…Pişkin and Polat [12] obtained the existence, both locally and globally in time, and the global nonexistence and asymptotic behavior of solutions for the Cauchy problem of a generalized Boussinesq-type equation with a damping term:…”

New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

“…Lump-type solutions and their interaction solutions are generated by Sadat [5]. In this context, various papers were presented to the literature [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The organization of this paper is as follows: firstly, we give the methodology of the improved Bernoulli sub-equation function method.…”

Blow-up for the sixth-order multidimensional generalized Boussinesq equation with arbitrarily high initial energy

“…Wang [19] considered equation (1.11) and obtained the well-posedness of solution, blow-up of solution with high initial energy, and the asymptotic behavior of the solution by using the multiplier method. Piskin and Polat [20] considered the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term…”