Geodesic
Blow-up of solutions of non-linear equations of Kadomtsev--Petviashvili and Zakharov--Kuznetsov types
Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 500-530

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Kadomtsev–Petviashvili equation, Zakharov–Kuznetsov equation, blow-up of solutions, non-linear capacity method. 
@article{IM2_2014_78_3_a4,
     author = {M. O. Korpusov and A. G. Sveshnikov and E. V. Yushkov},
     title = {Blow-up of solutions of non-linear equations of {Kadomtsev--Petviashvili} and {Zakharov--Kuznetsov} types},
     journal = {Izvestiya. Mathematics },
     pages = {500--530},
     publisher = {mathdoc},
     volume = {78},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a4/}
}
TY  - JOUR
AU  - M. O. Korpusov
AU  - A. G. Sveshnikov
AU  - E. V. Yushkov
TI  - Blow-up of solutions of non-linear equations of Kadomtsev--Petviashvili and Zakharov--Kuznetsov types
JO  - Izvestiya. Mathematics 
PY  - 2014
SP  - 500
EP  - 530
VL  - 78
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a4/
LA  - en
ID  - IM2_2014_78_3_a4
ER  - 
%0 Journal Article
%A M. O. Korpusov
%A A. G. Sveshnikov
%A E. V. Yushkov
%T Blow-up of solutions of non-linear equations of Kadomtsev--Petviashvili and Zakharov--Kuznetsov types
%J Izvestiya. Mathematics 
%D 2014
%P 500-530
%V 78
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a4/
%G en
%F IM2_2014_78_3_a4
M. O. Korpusov; A. G. Sveshnikov; E. V. Yushkov. Blow-up of solutions of non-linear equations of Kadomtsev--Petviashvili and Zakharov--Kuznetsov types. Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 500-530. http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a4/