Geodesic
Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains
Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1147-1170

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

We establish conditions sufficient for the absence of global solutions of semilinear hyperbolic inequalities and systems in conic domains of the Euclidean space $\mathbb R^N$. We consider a model problem in a cone $K$: that given by the inequality $$ \dfrac{\partial^2u}{\partial t^2}-\Delta u\geqslant |u|^q, \qquad (x,t)\in K\times(0,\infty), $$ The proof is based on the test-function method developed by Veron, Mitidieri, Pokhozhaev, and Tesei. 
@article{IM2_2002_66_6_a3,
     author = {G. G. Laptev},
     title = {Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains},
     journal = {Izvestiya. Mathematics },
     pages = {1147--1170},
     publisher = {mathdoc},
     volume = {66},
     number = {6},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a3/}
}
TY  - JOUR
AU  - G. G. Laptev
TI  - Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains
JO  - Izvestiya. Mathematics 
PY  - 2002
SP  - 1147
EP  - 1170
VL  - 66
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a3/
LA  - en
ID  - IM2_2002_66_6_a3
ER  - 
%0 Journal Article
%A G. G. Laptev
%T Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains
%J Izvestiya. Mathematics 
%D 2002
%P 1147-1170
%V 66
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a3/
%G en
%F IM2_2002_66_6_a3
G. G. Laptev. Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains. Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1147-1170. http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a3/