Hyperbolic equation with singular coefficient

Abstract

Dedicated to research existence conditions of quasi-linear differential equations with measurable coefficients, ie the study limitations imposed by the non linearity in which the system will have to research a solution and uniqueness of the solution of a certain class of functions. We consider weak solvability of quasi-linear differential partial differential equations of hyperbolic type with smooth and measurable singular coefficients, research methods based on the theory of semigroups using the method of differential forms. A new class of operators $A_\lambda^p:W_ 1 ^p \rightarrow W_ -1 ^p$ associated with a given differential equation and investigate the properties of these operators.