21 citations · 43 across the 19 of their papers we have counts for
16 papers · 1 filter
Long-time behaviour of a nonlocal stochastic fractional reaction--diffusion equation arising in tumour dynamics
Nikos I. Kavallaris, Subramani Sankar, Manil T. Mohan +2
We introduce a stochastic nonlocal reaction--diffusion model arising in tumour dynamics. Spatial dispersal is described by the fractional Laplacian, accounting for anomalous diffus…
A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation
Marvin Fritz, Nikos I. Kavallaris
We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035…
The Gierer-Meinhardt system in the entire space with non-local proliferation rates
Marius Ghergu, Nikos I. Kavallaris, Yasuhito Miyamoto
In this work, we present a novel stationary Gierer-Meinhardt system incorporating non-local proliferation rates, defined as follows: $$ \begin{cases} \displaystyle -Δu+λu=\frac{J*u…
Blowup solutions for the shadow limit model of singular Gierer-Meinhardt system with critical parameters
G. K. Duong, T. E. Ghoul, N. I. Kavallaris +1
We consider a nonlocal parabolic PDE, which may be regarded as the standard semilinear heat equation with power nonlinearity, where the nonlinear term is divided by some Sobolev no…
Impacts of noise on quenching of some models arising in MEMS technology
Ourania Drosinou, Nikos I. Kavallaris, Christos V. Nikolopoulos
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-Mec…
Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer-Meinhardt system
G. Ky Duong, Nikos I. Kavallaris, Hatem Zaag
In the current paper, we provide a thorough investigation of the blowing up behaviour induced via diffusion of the solution of the following non local problem \begin{equation*} \le…
Bifurcation diagram of a Robin boundary value problem arising in MEMS
Jong-Shenq Guo, N. I. Kavallaris, Chi-Jen Wang +1
We consider a parabolic problem with Robin boundary condition which arises when the edge of a micro-electro-mechanical-system (MEMS) device is connected with a flexible nonideal su…
A study of a nonlocal problem with Robin boundary conditions arising from MEMS technology
Ourania Drosinou, Nikos I. Kavallaris, Christos V. Nikolopoulos
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-Electr…
Diffusion-driven blow-up for a non-local Fisher-KPP type model
Nikos I. Kavallaris, Evangelos A. Latos
The purpose of the current paper is to unveil the key mechanism which is responsible for the occurrence of {\it Turing-type instability} for a non-local Fisher-KPP type model. In p…
Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain
Nikos. I. Kavallaris, Raquel Barreira, Anotida Madzvamuse
The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt model on an isotropically evolv…
A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass
Nikos I. Kavallaris, Tonia Ricciardi, Gabriella Zecca
We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted vs. repelled by a single chemical substa…
On the dynamics of a non-local parabolic equation arising from the Gierer-Meinhardt system
Nikos I. Kavallaris, Takashi Suzuki
The purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activator-inhibitor system known as a Gierer-Meinhardt model. Shad…
On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control
Nikos Kavallaris, Andrew Lacey, Christos Nikolopoulos
We consider a nonlocal parabolic model for a micro-electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solut…
On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics
Nikos I. Kavallaris, Johannes Lankeit, Michael Winkler
We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u Δu + u \int_Ω|\nabla u|^2 \] in bounded domains $Ω\subset\mathbb{R…
Finite-time blow-up of a non-local stochastic parabolic problem
Nikos I. Kavallaris, Yubin Yan
The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existen…
Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk
Nikos Kavallaris, Philippe Souplet
We consider a special case of the Patlak-Keller-Segel system in a disc, which arises in the modelling of chemotaxis phenomena. For a critical value of the total mass, the solutions…