Related papers: Generalized principal eigenvalues for heterogeneou…
We consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a {\it field} and a {\it road} in a population dynamics context) and coupled through exchange…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
The coexistence of effects in a certain class of generalized probability theories is investigated. The effect space corresponding to an even-sided regular polygon state space has a central hyperplane that contains all the nontrivial…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by…
We state a precise formulation of a conjecture concerning the product of the principal eigenvalue and the sup-norm of the landscape function of the Anderson model restricted to a large box. We first provide the asymptotic of the principal…
By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…
This paper is a continuation of [2] where a new model of biological invasions in the plane directed by a line was introduced. Here we include new features such as transport and reaction terms on the line. Their interaction with the pure…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
In this paper we exploit the phenomenon of two principal half eigenvalues in the context of fully nonlinear Lane-Emden type systems with possibly unbounded coefficients and weights. We show that this gives rise to the existence of two…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…
A Gelfand triplet for the Hamiltonian H of the Friedrichs model on R with finite-dimensional multiplicity space K, is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix) are (generalized) eigenvalues of…
In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place special emphasis on the associated first eigenvalue problem,…
Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
The Poisson-Nernst-Planck (PNP) diffusional model for the immittance or impedance spectroscopy response of an electrolytic cell in a finite-length situation is extended to a general framework. In this new formalism, the bulk behavior of the…
In [Adv. Math., 267(2014), 277-306], Cheskidov and Lu develop a new framework of the evolutionary system that deals directly with the notion of a uniform global attractor due to Haraux, and by which a trajectory attractor is able to be…