Long-time behaviour of the approximate solution to quasi-convolution Volterra equations
The integral representation of some biological phenomena consists in Volterra equations whose kernels involve a convolution term plus a non convolution one. Some significative applications arise in linearised models of cell migration and collective motion, as described in Di Costanzo et al. (Discrete Contin. Dyn. Syst. Ser. B 25 (2020) 443-472), Etchegaray et al. (Integral Methods in Science and Engineering (2015)), Grec et al. (J. Theor. Biol. 452 (2018) 35-46) where the asymptotic behaviour of the analytical solution has been extensively investigated.