International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 53, Pages 3373-3383
doi:10.1155/S0161171203208073
Applications of one- and two-dimensional
Volterra inequalities in differential equations of the
hyperbolic type
Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, Poznań 60-965, Poland
Received 14 August 2002
Copyright © 2003 Lechosław Hącia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Some variants of one-dimensional and two-dimensional integral
inequalities of the Volterra type are applied to study the
behaviour properties of the solutions to various boundary value
problems for partial differential equations of the
hyperbolic type. Moreover, new types of integral inequalities for
one and two variables, being a generalization of the Gronwall
inequality, are presented and used in the theory of nonlinear
hyperbolic differential equations.