Nonlinear singular hyperbolic initial boundary value problems
Texas State University, Department of Mathematics
In this article, we aim to prove the well posedness of a one point initial boundary value problem for a nonlinear hyperbolic singular integro-differential partial differential equation. Our proofs are mainly based on a fixed point theorem and some a priori bounds. The solvability of the problem is proved when the given data are related to a weighted Sobolev space. An additional result may allow us to study the regularity of the solution.
Fixed point theorem, A priori bound, Existence and uniqueness, Integro-differential equation
Mesloub, S., & Bachar, I. (2017). Nonlinear singular hyperbolic initial boundary value problems. <i>Electronic Journal of Differential Equations, 2017</i>(277), pp. 1-11.