In this study, we present infinite field behaviors for a class of integral equations with weakly singular kernels (Abel type) based on the methods for integro-differential equations in paper [1]. This class of integro-differential equations originated from an aeroelasticity problem [2]. After taking derivatives on the integral equations, equations are in the form of integro-differential equations. By separating variables, choosing splines as basis, interchanging the differentiation and integration of the integro-differential parts, we are able to compute the infinite behaviors of solutions by steps and discover that the possible behaviors depend on a specific formation of the initial conditions. We conclude the main result as a theorem.

infinite field, weakly singular, integro-differential equations.

Received: January 1, 2022; Accepted: February 10, 2022; Published: March 8, 2022

How to cite this article: Terry Herdman and Shihchung Chiang, On the infinite field of a class of weakly singular integral equations, Far East Journal of Dynamical Systems 34 (2022), 11-23. http://dx.doi.org/10.17654/0972111822002

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

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