Related papers: Time adaptive numerical solution of a highly degen…
We analyze the two-species reaction-diffusion system including trapping reaction $A + B \to A$ as well as coagulation/annihilation reactions $A + A \to (A,0)$ where particles of both species are performing L\'evy flights with control…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
This paper concerns with the large time behavior of solutions to a diffusion approximation radiation hydrodynamics model when the initial data is a small perturbation around an equilibrium state. The global-in-time well-posedness of…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…
The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
A practical correction formula relating the self-diffusion coefficient of dense liquids from molecular dynamics simulations with periodic boundary conditions to the self-diffusion coefficient in the thermodynamic limit is discussed. This…
We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through…
We focus on a highly nonlinear evolutionary abstract PDE system describing volume processes coupled with surfaces processes in thermoviscoelasticity, featuring the quasi-static momentum balance, the equation for the unidirectional evolution…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved…
In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using time- and space-dependent velocity fields as the control parameters. This partial differential equation (PDE)…
The variable two-step backward differentiation formula (BDF2) is revisited via a new theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and a class of orthogonal convolution kernels. We prove that, if the…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…