6 papers
A Unified Model for Blood and Lymph Flow with Coupled Nonsmooth Biochemical Dynamics
Bogna Jaszczak-Dyka, Åukasz PÅociniczak
We present a unified mathematical framework for modeling blood and lymph flow in biological vessels, with a particular focus on lymph transport through lymphangions. Starting from…
Parareal in time and spectral in space fast L1 quasilinear subdiffusion solver
Josefa Caballero, Åukasz PÅociniczak, Kishin Sadarangani
We consider the initial-boundary value problem for a quasilinear time-fractional diffusion equation, and develop a fully discrete solver combining the parareal algorithm in time wi…
Generalized capillary-rise models: existence and fast solvers in integral Hölder spaces
Josefa Caballero, Åukasz PÅociniczak, Kishin Sadarangani
We study a class of nonlinear Volterra integral equations that generalize the classical capillary rise models, allowing for nonsmooth kernels and nonlinearities. To accommodate suc…
Functional equation arising in behavioral sciences: solvability and collocation scheme in Hölder spaces
Josefa Caballero, Hanna OkrasiÅska-PÅociniczak, Åukasz PÅociniczak +1
We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a con…
Collocation method for a functional equation arising in behavioral sciences
Josefa Caballero, Hanna OkrasiÅska-PÅociniczak, Åukasz PÅociniczak +1
We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a…
Existence and uniqueness of solutions in the Lipschitz space of a functional equation and its application to the behavior of the paradise fish
Josefa Caballero, Åukasz PÅociniczak, Kishin Sadarangani
In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions…