3 papers
math.NA2022
Numerical scheme for Erdélyi-Kober fractional diffusion equation using Galerkin-Hermite method
Łukasz Płociniczak, Mateusz Świtała
The aim of this work is to devise and analyse an accurate numerical scheme to solve Erdélyi-Kober fractional diffusion equation. This solution can be thought as the marginal pdf of…
math.CA2019
Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise
Łukasz Płociniczak, Mateusz Świtała
We are concerned with the asymptotics and perturbation analysis of a singular second-order nonlinear ODE that models capillary rise of a fluid inside a narrow vertical tube. We pro…
math.AP2018
Compactly supported solution of the time-fractional porous medium equation on the half-line
Łukasz Płociniczak, Mateusz Świtała
In this work we prove that the time-fractional porous medium equation on the half-line with Dirichlet boundary condition has a unique compactly supported solution. The approach we…