Small amplitude solutions of the generalized IMBq equation

By Shubin Wang, Guowang Chen. 2002

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On the asymptotic behavior of solution for the generalized IBq equation with hydrodynamical damped term (2012, background): “Wang and Chen [5,28,29] studied the existence, both locally and globally in time, and nonexistence of solutions, and the global existence of small amplitude solutions for the Cauchy problem of the multidimensional generalized IMBq equation utt − u − utt = f (u).”
Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation (2009, background): “Wang and Chen [26] studied the existence and blow-up of the solution for the Cauchy problem of the generalized double dispersion equation utt − uxx − uxxtt + uxxxx − αuxxt = g(u)xx. (1.10) As seen from above explanations, the works on the multidimensional Boussinesq type equation relatively scarce i”
On small amplitude solutions to the generalized Boussinesq equations (2006, methodology): “Now for the last integral we use the estimate (see [39]) that if a, b ≥ 0 and max(a, b) > 1, then ∣∣∣∣ ∫ t 0 (1 + |t− t′|)−a(1 + |t′|)−b dt′ ∣∣∣∣ .”