Ulam-Hyers stability of Darboux-Ionescu problem

In his doctoral thesis, D. V. Ionescu has considered Darboux problem for partial differential equations of order two with modified argument. The Darboux-Ionescu problem was studied in some general cases by I. A. Rus. In this paper we study Ulam-Hyers stability and Ulam-Hyers-Rassias stability for this problem considered by I. A. Rus, using inequalities of Wendorff type.

THE DARBOUX AND KOSHI PROBLEM FOR LINEAR HYPERBOLIC EQUATIONS WITH CONSTANT COEFFICIENTS

Many phenomena of mechanics, physics, and biology are reduced to the study of hyperbolic equations. In order to describe these phenomena completely, the Darboux problem is posed for hyperbolic equations, and for further studies, an explicit representation of the problem under consideration is necessary. In this article discusses, we study the Darboux and Koshi problems for linear hyperbolic equations with constant coefficients.

A novel stability analysis for the Darboux problem of partial differential equations via fixed point theory

<abstract><p>We present Ulam-Hyers-Rassias (UHR) stability results for the Darboux problem of partial differential equations (DPPDEs). We employ some fixed point theorem (FPT) as the main tool in the analysis. In this manner, our results are considered as some generalized version of several earlier outcomes.</p></abstract>