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

Abstract

In this paper, we study the semi-Hyers–Ulam–Rassias stability and the generalized semi-Hyers–Ulam–Rassias stability of some partial differential equations using Laplace transform. One of them is the convection partial differential equation.

Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations

“…This method can be used successfully in the case of other equations with delay, integro-differential equations, partial differential equations or for fractional calculus. In [11], we have already studied a Volterra integro-differential equation of order I with a convolution type kernel and, in [12], the convection partial differential equation. In [20], the Poisson partial differential equation was studied via the double Laplace transform method.…”

“…In [12], the semi-Hyers-Ulam-Rassias stability of the convection partial differential equation was also studied using Laplace transform:…”

Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order

“…Based on [6,7,[12][13][14] we have constructed the Carleman matrix and based on it the approximate solution of the Cauchy problem for the matrix factorization of the Helmholtz equation. Boundary value problems, as well as numerical solutions of some problems, are considered in [30][31][32][33][34][35][36][37][38][39]. When solving correct problems, sometimes, it is not possible to find the value of the vector function on the entire boundary.…”

On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order

“…[ 10 ]. Boundary problems, as well as numerical solutions of some problems, are considered in works [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ].…”