相关论文: Asymptotic regimes of an integro-difference equati…
We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in…
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…
This paper proposes a ridgeless kernel method for solving infinite-horizon, deterministic, continuous-time models in economic dynamics, formulated as systems of differential-algebraic equations with asymptotic boundary conditions (e.g.,…
An integro-differential equation on a tree graph is used to model the evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
The paper deals with the large time asymptotic of the fundamental solution for a time fractional evolution equation for a convolution type operator. In this equation we use a Caputo time derivative of order $\alpha$ with $\alpha\in(0,1)$,…
The paper deals with an integrodifferential operator which models numerous phenomena in superconductivity, in biology and in viscoelasticity. Initialboundary value problems with Neumann, Dirichlet and mixed boundary conditions are analyzed.…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction…
We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space…
We consider an abstract first order evolution equation in a Hilbert space in which the linear part is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the…
In this work, we provide an asymptotic analysis of the solutions to an elliptic integro-differential equation. This equation describes the evolutionary equilibria of a phenotypically structured population, subject to selection, mutation,…
The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions.…
In this Note, we describe the stationary equilibria and the asymptotic behaviour of an heterogeneous logistic reaction-diffusion equation under the influence of autonomous or time-periodic forcing terms. We show that the study of the…
For a Nicholson's blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is…
This paper provide a comprehensive analysis of the finite and long time behavior of continuous-time non-Markovian dynamical systems, with a focus on the forward Stochastic Volterra Integral Equations(SVIEs).We investigate the properties of…
The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the…
We consider a nonlocal aggregation diffusion equation incorporating repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction. When the attractive interaction kernel is radially symmetric and strictly…
The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the…
An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…