Related papers: Effects of large degenerate advection and boundary…
This paper investigates the limit of the principal eigenvalue $\lambda(s)$ as $s\to+\infty$ for the following elliptic equation \begin{align*} -\Delta\varphi(x)-2s\mathbf{v}\cdot\nabla\varphi(x)+c(x)\varphi(x)=\lambda(s)\varphi(x), \quad…
Consider the eigenvalue problem of a linear second order elliptic operator: \begin{equation} \nonumber -D\Delta \varphi -2\alpha\nabla m(x)\cdot \nabla\varphi+V(x)\varphi=\lambda\varphi\ \ \hbox{ in }\Omega, \end{equation} complemented by…
In this article, we are concerned with the following eigenvalue problem of a linear second order elliptic operator: \begin{equation} \nonumber -D\Delta \phi -2\alpha\nabla m(x)\cdot \nabla\phi+V(x)\phi=\lambda\phi\ \ \hbox{ in }\Omega,…
In this paper we study, both numerically and analytically, the asymptotic behavior of the principal eigenfunction of \eqref{1.1}, normalized by \eqref{1.2}, as $s\uparrow +\infty$. Based on the numerical computations of this paper, we can…
There are numerous studies focusing on the convergence of the principal eigenvalue $\lambda(s)$ as $s\to+\infty$ corresponding to the elliptic eigenvalue problem \begin{align*}…
We investigate the effects of advection on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions. Various asymptotic behaviors of the principal eigenvalues, when advection coefficient…
The paper is concerned with the principal eigenvalue of some linear elliptic operators with drift in two dimensional space. We provide a refined description of the asymptotic behavior for the principal eigenvalue as the drift rate…
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…
In this paper, we consider the following principal eigenvalue problem with a large divergence-free drift: \begin{equation}\label{0.1} -\varepsilon\Delta \phi-2\alpha\nabla m(x)\cdot\nabla \phi+V(x)\phi=\lambda_\alpha \phi\ \,\ \text{in}\, \…
In this paper, we are concerned with the following eigenvalue problem with an advection term: \begin{equation}\label{0.1} \left\{ \begin{split} -\epsilon\Delta \phi-2\alpha\nabla m(x)\cdot\nabla \phi+V(x)\phi&=\lambda \phi\ \ \text{in}\ \…
This paper investigates the asymptotic behavior of the principal eigenvalue $\lambda(s)$, as $s\to+\infty$, for the following elliptic eigenvalue problem \begin{equation*}\label{E} -\Delta_{M}u-s\langle \nabla_M f, \nabla_M u\rangle_g +c…
We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that the principal eigenvalue decays exponentially under the…
We consider a periodic-parabolic eigenvalue problem with a non-negative potential $\lambda m$ vanishing on a non-cylindrical domain $D_m$ satisfying conditions similar to those for the parabolic maximum principle. We show that the limit as…
We establish the monotonicity of the principal eigenvalue $\lambda_1(A)$, as a function of the advection amplitude $A$, for the elliptic operator $L_{A}=-\mathrm{div}(a(x)\nabla)+A\mathbf{V}\cdot\nabla +c(x)$ with incompressible flow…
This paper is concerned with the asymptotic behavior of the generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media where one scale is fixed and another one…
We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…
For fixed $c\in\mathbb R$, $l>0$ and a general non-symmetric kernel function $J(x)$ satisfying a standard assumption, we consider the nonlocal diffusion operator \begin{align*} \bf{L}^{J,…
In this paper, we investigate an eigenvalue problem associated with an age-structured operator incorporating random diffusion and advection. Our primary focus is on examining the asymptotic behaviors of the principal eigenvalue with respect…
The spectral theory of the p-Laplacian is well developed for classical Dirichlet and Neumann boundary conditions, but the transitional Robin regime on exterior domains remains largely unexplored. This paper studies a weighted p-Laplacian…
The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are…