Remarks on the generalized Kadomtsev-Petviashvili equations. (English) Zbl 0814.35119

Saut, Jean-Claude

Indiana Univ. Math. J. 42, No. 3, 1011-1026 (1993).

The author studies the generalized KP equations \[ u_ t + u^ pu_ x + u_{xxx} + \varepsilon v_{y} = 0, \quad u_ y = v_ x. \] The aim is to investigate blow-up properties of solutions. The blow-up result concerns the case \(\varepsilon = - 1\) and \(p \geq 4\). The paper contains also results on local solvability.

Reviewer: A.Pankov (Vinnitsa)

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

blow-up; local solvability