The main purpose of this paper is to study the existence and properties of solutions of a certain nonlinear non-Lipschitz hyperbolic partial differential equation in two independent variables with irregular data. Using regularization techniques, we give a meaning to this problem by replacing it by a tow parameters family of Lipschitz regular problems. We prove existence and uniqueness of the solution in an appropriate algebra of generalized functions and we precise how it depends on the choices made. We study the relationship with the classical solution.
On a Nonlinear Hyperbolic Partial Differential Equation with Irregular Data,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
2, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss2/3