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In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…

Analysis of PDEs · Mathematics 2016-12-20 Sepideh Mirrahimi

We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…

Probability · Mathematics 2022-06-17 Nicolas Champagnat , Sylvie Méléard , Sepideh Mirrahimi , Viet Chi Tran

We study the macroscopic behavior of chemical reactions modeled as random time-changed Poisson processes on discrete state spaces. Using the WKB reformulation, the backward equation of the rescaled process leads to a discrete…

Analysis of PDEs · Mathematics 2025-09-26 Yuan Gao , Yuxi Han

We determine the large-time behavior of unbounded solutions for the so-called viscous Hamilton Jacobi equation, $u_t - \Delta u + |Du|^m = f(x)$, in the quadratic and subquadratic cases (i.e., for $1<m\leq 2$), with a particular focus on…

Analysis of PDEs · Mathematics 2021-11-09 Alexander Quaas , Andrei Rodríguez-Paredes

We study the statistics of extinction and blowup times in well-mixed systems of stochastically reacting particles. We focus on the short-time tail, $T \to 0$, of the extinction- or blowup-time distribution $\mathcal{P}_m(T)$, where $m$ is…

Statistical Mechanics · Physics 2026-04-14 Rotem Degany , Michael Assaf , Baruch Meerson

In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…

Probability · Mathematics 2018-05-30 Zhaolei Cui , Edward Omey , Wenyuan Wang , Yuebao Wang

We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…

Analysis of PDEs · Mathematics 2017-08-31 Taiga Kumagai

We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we…

Analysis of PDEs · Mathematics 2013-08-01 Emeric Bouin , Sepideh Mirrahimi

We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…

Probability · Mathematics 2026-01-12 Amjad Saef , Wilhelm Stannat

The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation.…

Optimization and Control · Mathematics 2021-02-09 Antonio Marigonda , Khai T. Nguyen

We study the large-time behavior of bounded from below solutions of parabolic viscous Hamilton-Jacobi Equations in the whole space $\mathbb{R}^N$ in the case of superquadratic Hamiltonians. Existence and uniqueness of such solutions are…

Analysis of PDEs · Mathematics 2020-04-07 Guy Barles , Alexander Quaas , Andrei Rodríguez

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish…

Analysis of PDEs · Mathematics 2015-05-30 Guy Barles , Hiroyoshi Mitake , Hitoshi Ishii

The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…

Probability · Mathematics 2017-11-29 Sergey Foss , Andrew Richards

We consider a population structured by a space variable and a phenotypical trait, submitted to dispersion, mutations, growth and nonlocal competition. This population is facing an environmental gradient: the optimal trait for survival…

Analysis of PDEs · Mathematics 2019-10-14 Gwenaël Peltier

We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…

Analysis of PDEs · Mathematics 2020-10-02 Hiroyoshi Mitake , Hung V. Tran , Truong-Son Van

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

Statistics Theory · Mathematics 2026-04-14 John H. J. Einmahl , Chen Zhou

Run and tumble equations are widely used models for bacterial chemotaxis. In this paper, we are interested in the long time behaviour of run and tumble equations with unbounded velocities. We show existence, uniqueness and quantitative…

Analysis of PDEs · Mathematics 2025-05-14 Émeric Bouin , Josephine Evans , Luca Ziviani

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

Probability · Mathematics 2010-07-07 Gyorgy Steinbrecher , Xavier Garbet , Boris Weyssow

Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…

Populations and Evolution · Quantitative Biology 2008-07-24 Tamar Friedlander , Naama Brenner

We study the asymptotic behavior of solutions to the Dirichlet problem for Hamilton-Jacobi equations with large drift terms, where the drift terms are given by the Hamiltonian vector fields of Hamiltonian $H$. This is an attempt to…

Analysis of PDEs · Mathematics 2019-12-20 Hitoshi Ishii , Taiga Kumagai