Ulam-Hyers-Rassias stability of some quasilinear partial differential equations of first order

Abstract

In this paper we investigate the Ulam-Hyers-Rassias stability for some quasilinear partial differential equations.

Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

“…Rassias in [15]. Ulam-Hyers stability of partial differential equations was also studied in [16][17][18][19][20][21]. In [22], Brzdek, Popa, Rasa and Xu presented a unified and systematic approach to the field.…”

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

“…Rassias. The Ulam-Hyers stability of partial differential equations was also studied in [21][22][23][24][25][26].…”

Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations

“…Rassias in [25] started the study of Hyers-Ulam stability of partial differential equations. These have also been studied in [26][27][28][29][30][31]. A summary of these issues can be found in the books [32,33].…”

“…A summary of these issues can be found in the books [32,33]. There are several ways to study Ulam stability, for example the direct method [6][7][8], the fixed point method [34,35], the integral inequalities method [36], the changes of variables method [26,29,30], and the integral transforms method. Laplace transform was used, for instance, in [37][38][39].…”