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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 53, Pages 3373-3383

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 Hindawi Publishing Corporation. 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.


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.