arXiv subjects

Christos V. Nikolopoulos

Publications and source records attributed to Christos V. Nikolopoulos.

5 recordsLinked to original sources

arXiv2026

Long-time behaviour of a nonlocal stochastic fractional reaction--diffusion equation arising in tumour dynamics

We introduce a stochastic nonlocal reaction--diffusion model arising in tumour dynamics. Spatial dispersal is described by the fractional Laplacian, accounting for anomalous diffusion and long--range relocation events. The system is perturbed by multiplicative fractional Brownian motion (fBm) with Hurst parameter $H>1/2$, which we interpret as temporally correlated fluctuations in the tumour microenvironment and host response. We first establish well--posedness and identify parameter regimes leading to global--in--time solutions or finite--time blow--up under general multiplicative fractional noise. We then focus on linear multiplicative noise and, via a Doss--Sussmann transformation, derive sharper results: explicit lower and upper bounds for the blow--up time together with quantitative estimates of the blow--up probability, clarifying how noise intensity can accelerate progression or, on favourable paths, enhance suppression consistent with extinction (loss of viability). Finally, one--dimensional simulations illustrate the interplay between anomalous diffusion, fractional noise, and the nonlocal reaction mechanism in shaping the long--time dynamics.

math.AP↗

arXiv2025

Quenching time and probability estimates for a stochastic reaction-diffusion system with coupled inner singular absorption terms driven by mixed noises

This paper investigates a stochastic parabolic system under Robin boundary conditions, for which the deterministic counterpart exhibits finite quenching. The stochastic system incorporates mixed noise, combining standard one-dimensional Brownian motion and fractional Brownian motion. Under appropriate assumptions, we derive explicit lower and upper bounds for the quenching time of the solution and establish the global existence of a weak solution. Leveraging Malliavin calculus, we further obtain a quantifiable lower and upper bound on the quenching probability. To complement the theoretical analysis, we design a numerical scheme tailored to the system and present results that validate the analytical predictions, offering insights into the interplay between noise and quenching behaviour.

math.PR↗

arXiv2021

A study of a nonlocal problem with Robin boundary conditions arising from MEMS technology

In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the steady-state problem in one dimension and we present some numerical results regarding its bifurcation diagram. Next the $N-$dimensional nonlocal problem steady-state problem is investigated and a Pohozaev-type identity is first obtained which then facilitates derivation of an estimate of the pull-in voltage for radially symmetric domains. Later the time-dependent problem is investigated and global-in-time as well as quenching results are obtained again for general and radially symmetric domains. We close the current work with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented verifying the obtained analytical results.

math.AP↗

arXiv2020

Impacts of noise on quenching of some models arising in MEMS technology

In the current work we study a stochastic parabolic problem. The underlying problem is actually motivated by the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of the potential difference controlling the device. We first present the mathematical model and then we deduce some local existence results. Next for some particular versions of the model, regarding its boundary conditions, we derive quenching results as well as estimations of the probability for such singularity to occur. Additional numerical study of the problem in one dimension follows, investigating the problem further with respect to its quenching behaviour.

math.AP↗

arXiv2019

Colloidal Transport in Locally Periodic Evolving Porous Media -- An Upscaling Exercise

We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow reducing therefore the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and therefore, can provide estimates on the storage capacity of the porous matrix.

math.AP↗