International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 53, Pages 3373-3383
doi:10.1155/S0161171203208073
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.