On some new integral and integrodifferential inequalities in two independent variables and their applications

In this paper an elementary method used in a recent paper by Snow will be used to establish some new inequalities of the Gronwall type in two independent variables. The resultant new class of inequalities will bring a great number of inequalities under one proof, so to speak, and may in general, be applied to a class of nonlinear partial integrodifferential equations of the hyperbolic type, to study the uniqueness, continuous dependence, stability and numerical computations.