相关论文: The optimal initial datum for a class of reaction-…

The first part of this paper is devoted to the derivation of a technical result, related to the stability of the solution of a reaction-diffusion equation $u_t-\Delta u = f(x,u)$ on $(0,\infty)\times \mathbb{R}^N$, where the initial datum…

In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a constructive method, alternating minimizing movements for the…

Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assumptions, we prove that radial solutions of the evolution…

In this article, we study the optimization of resource distributions in a one-dimensional logistic diffusive model. The goal is to determine a distribution on a bounded one-dimensional domain that maximizes the total population at…

Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…

In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal…

The dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and…

In the spirit of the macroscopic crowd motion models with hard congestion (i.e. a strong density constraint $\rho\leq 1$) introduced by Maury {\it et al.} some years ago, we analyze a variant of the same models where diffusion of the agents…

Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…

This article is accepted for publication in the "Annals I.H.P. Prob. & Stat.". We investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T') of the discrete setting, cf.…

We identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance to the last-passage time $\gamma_z$ to a given level $z>0$, for an arbitrary non-negative time-homogeneous transient diffusion $X$. We demonstrate that $\tau_*$…

How diffusion impacts on ecological dynamics under the Allee effect and spatial constraints? That is the question we address. Employing a microscopic minimal model in a metapopulation (without imposing nonlinear birth and death rates) we…

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…

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…

Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$,…

Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…

Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…

In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…

We introduce a general-purpose method for optimising the mixing rate of advective fluid flows. An existing velocity field is perturbed in a $C^1$ neighborhood to maximize the mixing rate for flows generated by velocity fields in this…

We consider the problem of identifying a sparse initial source condition to achieve a given state distribution of a diffusion-advection partial differential equation after a given final time. The initial condition is assumed to be a finite…