Gronwall's Vector Inequality and its Application to a Class of Non-Self-Adjoint Linear and Non-Linear Hyperbolic Partial Differential Equations

Stimulating research works have been undertaken ([1], [2], [5], [6], [8], [10]) to generalize the original form of Gronwall's inequality [3], [7] due to its importance in the study of differential equations. The works done so far, can be employed to investigate different properties of ordinary differential equations and some self-adjoint [8] partial differential equations of hyperbolic type. However, our work [5] is applicable to non-self adjoint cases in two dimensions.