Related papers: A General Inverse Problem for the Growth-Fragmenta…
In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution $(\lb,\U,\phi)$ to the related eigenproblem. Such eigenelements are…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…
It is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system.…
We further develop the general theory of the area reactivity model that provides an alternative description of the diffusion-influenced reaction of an isolated receptor-ligand pair in terms of a generalized Feynman-Kac equation. We analyze…
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a…
This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…
This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation…
Telomeres are repetitive sequences situated at both ends of the chromosomes of eukaryotic cells. At each cell division, they are eroded until they reach a critical length that triggers a state in which the cell stops to divide: the…
Phase separation is not only ubiquitous in diverse physical systems, but also plays an important organizational role inside biological cells. However, experimental studies of intracellular condensates (drops with condensed concentrations of…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert…
As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the…
We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…