On Ulam–Hyers Stability for a System of Partial Differential Equations of First Order

Abstract

The aim of this paper is to investigate generalized Ulam–Hyers stability and generalized Ulam–Hyers–Rassias stability for a system of partial differential equations of first order. More precisely, we consider a system of two nonlinear equations of first order with an unknown function of two independent variables, which satisfy the corresponding compatibility condition. The study method is that of differential inequalities of the Gronwall type.

Global existence and stability results for a time-fractional diffusion equation with variable exponents

“…Andras et al [6] studied Ulam-Hyers stability of first order differential system with non-local condition. Marian et al [29] provided a stability result for a system of partial differential equation using the Gronwall inequality and the fixed point technique.…”

Hyers–Ulam Stability of a System of Hyperbolic Partial Differential Equations

“…Ulam stability of systems of differential equations began with the paper by Prastaro and Rassias [22]. Systems have also been studied, for example, in [23,24].…”

Semi-Hyers–Ulam–Rassias Stability of the Convection Partial Differential Equation via Laplace Transform

“…The field continued to develop rapidly. Linear differential equations were studied in [5][6][7], integral equations in [8], delay differential equations in [9], linear difference equations in [10,11], other equations in [12], and systems of differential equations in [13]. A summary of these results can be found in [14].…”