This article is cited in 8 papers

Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains

G. G. Laptev

Tula State University

Abstract: 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.

UDC: 517.9

MSC: 35J60, 35G20, 35B99, 35J65, 35B50

Received: 26.03.2001

DOI: 10.4213/im410

 English version: Izvestiya: Mathematics, 2002, 66:6, 1147–1170

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