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mathematicsArticleSemi-Hyers lam assias Stability on the Convection GNF6702 References partial Differential Equation via Laplace TransformDaniela MarianDepartment of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania; [email protected],Abstract: Within this paper, we study the semi-Hyers lam assias stability plus the generalized semiHyers lam assias stability of some partial differential Benidipine Protocol equations working with Laplace transform. One of them is the convection partial differential equation. Keywords and phrases: semi-Hyers lam assias stability; generalized semi-Hyers lam assias stability; Laplace transform; convection partial differential equation MSC: 44A10; 35B1. Introduction It is actually well known that the study of Ulam stability began in 1940, with a difficulty posed by Ulam regarding the stability of homomorphisms [1]. In 1941, Hyers [2] gave a partial answer inside the case in the additive Cauchy equation in Banach spaces. After that, Obloza [3] and Alsina and Ger [4] began the study with the Hyers lam stability of differential equations. The field continued to create rapidly. Linear differential equations were studied in [5], integral equations in [8], delay differential equations in [9], linear distinction equations in [10,11], other equations in [12], and systems of differential equations in [13]. A summary of these outcomes might be discovered in [14]. The Hyers lam stability of linear differential equations was studied applying the Laplace transform by H. Rezaei, S. M. Jung, and Th. M. Rassias [15], and by Q. H. Alqifiary and S. M. Jung [16]. This method was also used in [179]. The study of the stability of partial differential equations began in 2003, with all the paper [20] of A. Prastaro and Th.M. Rassias. The Ulam yers stability of partial differential equations was also studied in [216]. In [27], M. N. Qarawani applied the Laplace transform to establish the Hyers lam assiasGavruta stability of initial-boundary worth dilemma for heat equations on a finite rod: u two u = a2 two , t 0, 0 x l. t x In [28], D.O. Deborah and a. Moyosola studied nonlinear, nonhomogeneous partial differential equations using the Laplace differential transform technique: d2 w( x, t) + an ( x ) Rw( x, t) + bn ( x )Sw( x, t) = f ( x, t), t 0, x 0, n N, dt2 where an ( x ), bn ( x ) are variable coefficients, n N, R would be the linear operator, S could be the nonlinear operator, and f ( x, t) would be the source function. In [29], E. Bicer used the Sumudu transform to study the equation: yt – ky xx = 0, k a positive genuine constant, ( x, t) D, D = ( x0 , x ] (0, ).Citation: Marian, D. Semi-Hyers lam assias Stability of the Convection Partial Differential Equation by way of Laplace Transform. Mathematics 2021, 9, 2980. https:// doi.org/10.3390/math9222980 Academic Editor: Janusz Brzd k e Received: 23 October 2021 Accepted: 20 November 2021 Published: 22 NovemberPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.Copyright: 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is definitely an open access post distributed beneath the terms and situations from the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ four.0/).Mathematics 2021, 9, 2980. https://doi.org/10.3390/mathhttps://www.mdpi.com/journal/mathemat.
