Related papers: Grow-up rate and refined asymptotics for a two-dim…
Probes of cosmic expansion constitute the main basis for arguments to support or refute a possible apparent acceleration due to different expansion rates in the universe as described by inhomogeneous cosmological models. We present in this…
Spectral functions of the pseudoscalar $D$ meson in the nuclear medium are analyzed using QCD sum rules and the maximum entropy method. This approach enables us to extract the spectral functions without any phenomenological assumption, and…
We study the behaviour of nonnegative solutions to the quasilinear heat equation with a reaction localized in a ball $$ u_t=\Delta u^m+a(x)u^p, $$ for $m>0$, $0<p\le\max\{1,m\}$, $a(x)=\mathds{1}_{B_L}(x)$, $0<L<\infty$ and $N\ge2$. We…
It is well known that solutions to the Patlak--Keller--Segel system on $\mathbb{R}^2$ blow up in finite time if the initial mass exceeds $8\pi$. In this paper, we investigate the mixing effect induced by a Couette flow $(Ay, 0)$ with a…
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are…
In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants,…
We study a chemotaxis-growth system with nonlinear local and nonlocal reactions and gradient-dependent damping. Under suitable conditions on the system parameters and spatial dimension, we prove that solutions exist globally in time and…
For a competition-diffusion blow-up system involving the fractional Laplacian of the form \begin{equation*}\label{syst1} -(-\Delta)^su=uv^2,\quad-(-\Delta)^sv=vu^2,\quad u,v>0 \ \mathrm{in} \ \mathbb{R}^N, \end{equation*} whith $s\in(0,1)$,…
Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infection sites. Mathematically chemotaxis is described by the…
We give a conjecture for the asymptotic growth rate of the number of indecomposable summands in the tensor powers of representations of finite monoids, expressing it in terms of the (Brauer) character table of the monoid's group of units.…
The present work proceeds to consider the convergence of the solutions to the following doubly degenerate chemotaxis-consumption system \begin{align*} \left\{ \begin{array}{r@{\,}l@{\quad}l@{\,}c} &u_{t}=\nabla\cdot\big(u^{m-1}v\nabla…
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…
We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity. This asymptotics creates a time scale separation which results in the…
We study solutions of a Euclidean weighted porous medium equation when the weight behaves at spacial infinity like $|x|^{-\gamma}$, for $\gamma\in [0,2)$, and is allowed to be singular at the origin. In particular we show local-in-time…
We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided…
We present a new model of giant planet formation that extends the core-accretion model of Pollack etal (1996) to include migration, disc evolution and gap formation. We show that taking into account these effects can lead to a much more…
We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation,…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
A simple proof of concentration of mass equal to $8\pi$ for blowing up $N$-symmetric solutions of the Keller--Segel model of chemotaxis in two dimensions with large $N$ is given. Moreover, a criterion for blowup of solutions in terms of the…
In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a…