90 citations · 188 across the 16 of their papers we have counts for
20 papers
The GLEAM 4-Jy (G4Jy) Sample: V. Broadband spectral analysis
Sarah V. White, Siegfried A. Gawenda, Giulia Macario +6
The G4Jy Sample consists of 1,863 of the brightest sources in the southern sky, as selected at 151 MHz using the GaLactic and Extragalactic All-sky MWA (GLEAM) survey. We supplemen…
Time-fractional porous medium equation: Erdélyi-Kober integral equations, compactly supported solutions, and numerical methods
Belen López, Hanna Okrasińska-Płociniczak, Łukasz Płociniczak +1
The time-fractional porous medium equation is an important model of many hydrological, physical, and chemical flows. We study its self-similar solutions, which make up the profiles…
The Bushell-Okrasiński inequality
Łukasz Płociniczak
We present an expository account of the Bushell-Okrasiński inequality, the motivation behind it, its history, and several generalizations. This inequality originally appeared in st…
Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data
Łukasz Płociniczak
We investigate the error of the (semidiscrete) Galerkin method applied to a semilinear subdiffusion equation in the presence of a nonsmooth initial data. The diffusion coefficient…
On a discrete composition of the fractional integral and Caputo derivative
Łukasz Płociniczak
We prove a discrete analogue for the composition of the fractional integral and Caputo derivative. This result is relevant in numerical analysis of fractional PDEs when one discret…
Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology
Łukasz Płociniczak
A special place in climatology is taken by the so-called conceptual climate models. These relatively simple sets of differential equations can successfully describe single mechanis…
Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line
Hanna Okrasińska-Płociniczak, Łukasz Płociniczak
Many physical, biological, and economical systems exhibit various memory effects due to which their present state depends on the history of the whole evolution. Combined with the n…
Stability of fixed points in an approximate solution of the spring-mass running model
Zofia Wróblewska, Piotr Kowalczyk, Łukasz Płociniczak
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large…
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…
A weighted finite difference method for subdiffusive Black Scholes Model
Grzegorz Krzyżanowski, Marcin Magdziarz, Łukasz Płociniczak
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in…
Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model
Łukasz Płociniczak
We construct a dynamical system based on the KCG (Källén, Crafoord, Ghil) conceptual climate model which includes the ice-albedo and precipitation-temperature feedbacks. Further, w…
Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting
Łukasz Płociniczak
In this short note we consider a nonlinear and spatially nonlocal PDE modelling moisture evolution in a porous medium. We then show that it naturally arises as a description of sup…
Numerical method for the time-fractional porous medium equation
Łukasz Płociniczak
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits bot…
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…
Hopf bifurcation in a conceptual climate model with ice-albedo and precipitation-temperature feedbacks
Łukasz Płociniczak
In this paper we analyse a dynamical system based on the so-called KCG (Källén, Crafoord, Ghil) conceptual climate model. This model describes an evolution of the globally averaged…
Quickest drift change detection in Lévy-type force of mortality model
Michał Krawiec, Zbigniew Palmowski, Łukasz Płociniczak
In this paper we give solution to the quickest drift change detection problem for a Lévy process consisting of both a continuous Gaussian part and a jump component. We consider her…
Finite difference method for a Volterra equation with a power-type nonlinearity
Hanna Okrasińska-Płociniczak, Łukasz Płociniczak
In this work we prove that a family of explicit numerical finite-difference methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity. In t…
Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
Łukasz Płociniczak
In this paper we investigate the porous medium equation with a fractional temporal derivative. We justify that the resulting equation emerges when we consider the waiting-time (or…
On fractional Bessel equation and the description of corneal topography
Wojciech Okrasiński, Łukasz Płociniczak
In this note we apply a modified fractional Bessel differential equation to the problem of describing corneal topography. We find the solution in terms of the power series. This so…
Bessel Function Model for Corneal Topography
Wojciech Okrasiński, Łukasz Płociniczak
In this paper we consider a new nonlinear mathematical model for corneal topography formulated as two-point boudary value problem. We derive it from first physical principles and p…