相关论文: A priori estimates for excitable models
In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh--Nagumo and FitzHugh--Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such…
We consider an interacting system of particles with value in $\mathbb{R}^d \times \mathbb{R}^d$, governed by transport and diffusion on the first component, on that may serve as a representative model for kinetic models with a degenerate…
In this paper, we use a Banach fixed point theorem to obtain suficient conditions satisfying the convergence and exponential convergence of solutions for the linear system of advanced differential equations. The considered system with…
A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
This paper studies the solutions of a reaction--diffusion system with nonlinearities that generalise the Lengyel--Epstein and FitzHugh--Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the…
For the principal eigenvalue with bilateral Dirichlet boundary condition, the so-called basic estimates were originally obtained by capacitary method. The Neumann case (i.e., the ergodic case) is even harder, and was deduced from the…
We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic…
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann…
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…
For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a…
The present article is devoted to the 3D dissipative quasi-geostrophic system (QG). This system can be obtained as limit model of the Primitive Equations in the asymptotics of strong rotation and stratification, and involves a non-radial,…
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
A general FitzHugh-Rinzel model, able to describe several neuronal phenomena, is considered. Linear stability and Hopf bifurcations are investigated by means of the spectral equation for the ternary autonomous dynamical system and the…
We discuss several qualitative properties of the solutions of reaction-diffusion systems and equations of the form $u_t = \epsilon^2 D \Delta u + f(u,x,\epsilon t)$, that are used in modeling pattern formation. We analyze the diffusion…
Given a solution of a semilinear dispersive partial differential equation with a real analytic nonlinearity, we relate its Cauchy data at two different times by nonlinear representation formulas in terms of convergent series. These series…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or…