Seminario Rubio de Francia: “Analysis and approximation of a weakly singular Volterra integral equation with nonlinear exponent”.- Jueves 4 de diciembre
El jueves 4 de diciembre de 2025 a las 12:10 h tendrá lugar una nueva sesión del ciclo de Seminarios Rubio de Francia de la Universidad de Zaragoza del curso 2025/2026 con Martin Stynes (Beijing Computational Science Research Center and Ocean University of China, Qingdao). Impartirá el seminario de título “Analysis and approximation of a weakly singular Volterra integral equation with nonlinear exponent”.
La charla tendrá lugar en el Seminario Rubio de Francia (edificio de Matemáticas, primera planta) de la Facultad de Ciencias, Universidad de Zaragoza. El seminario se podrá seguir en directo a través del enlace: https://www.youtube.com/@seminariorubiodefrancia.
Resumen (en inglés):
A weakly singular Volterra integral equation (VIE) whose kernel has a nonlinear exponent a(u(s)) is considered. After showing the compactness of the nonlinear Volterra integral operator, we apply Schaefer's fixed-point theorem to establish existence of a continuous solution u(t) to the VIE. Uniqueness and regularity of this solution are then proved; it has a weak singularity at the initial time t=0 that is characterised by a(u(0)) A nonlinear collocation method is constructed on uniform and graded meshes. Well-posedness and stability of this method are shown, and an estimate of its error, which is sharp up to a log factor, is derived using completely novel techniques. Numerical experiments support the theoretical findings.
Toda la información en: http://anamat.unizar.es/seminario.htm
