Existence and Hyers-Ulam stability of solutions for a delayed hyperbolic partial differential equation - Celik, Canan; Develi, Faruk (SPRINGER, 2022)
In this paper, we first prove the existence and uniqueness of the solutions for a delayed hyperbolic partial differential equation by applying the progressive contraction technique introduced by Burton (Nonlinear Dyn Syst Theory 16(4): 366-371, 2016; Fixed Point Theory 20(1): 107-113, 2019) to the corresponding fixed-point problem. Then we derive a Hyers-Ulam stability result for this differential equation by using a Wendorff-type inequality and the Abstract Gronwall Lemma.
Keywords: Progressive contractions; Hyperbolic partial differential equation; Hyers-Ulam stability; Fixed point theory; 1ST-ORDER; OPERATOR; Mathematics