Blow-up of solutions of non-linear equations of Kadomtsev–Petviashvili and Zakharov–Kuznetsov types

Abstract

The Kadomtsev–Petviashvili equation and Zakharov–Kuznetsov equation are important in physical applications. We obtain sufficient conditions for finite-time blow-up of solutions of these equations in bounded and unbounded domains. We describe how the initial data influence the blow-up time. To do this, we use the non-linear capacity method suggested by Pokhozhaev and Mitidieri and combine it with the method of test functions, which was developed in joint papers with Galaktionov. Note that our results are the first blow-up results for many equations in this class.