Related papers: Entire Solutions of Diffusive Lotka-Volterra Syste…
This paper studies the Lotka-Volterra competition model with cross-diffusion terms under homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of positive steady-states as equal two cross-diffusion coefficients tend…
Our interest here is to find the invader in a two species, diffusive and competitive Lotka-Volterra system in the particular case of travelling wave solutions. We investigate the role of diffusion in homogeneous domains. We might expect a…
This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial…
This paper studies forced waves for the heterogeneous Fisher-KPP equation $u_t = u_{xx} + u(a(x-ct)-u)$, where $c>0$ and $a(z)>0$ satisfies $a(-\infty)=\alpha>0=a(+\infty)$, $a'(z)\le0$ ($z\gg1$). Using ODE asymptotic analysis, we classify…
Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such constructed upper and lower…
We consider the Fisher-KPP reaction-diffusion equation in the whole space. We prove that if a solution has, to main order and for all times (positive and negative), the same exponential decay as a planar traveling wave with speed larger…
The KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(\beta-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\beta>1/3$). This equation admits ---…
We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem $$(-\Delta)^s u_i = f_i(x,u_i) - \beta u_i^p \sum_{j\neq i} a_{ij} u_j^p,$$ where $i = i,\dots, k$, $s\in(0,1)$,…
In this paper we consider the existence of standing waves for a coupled system of $k$ equations with Lotka-Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed…
Solutions of the Navier-Stokes and Euler equations with initial conditions for 2D and 3D cases were obtained in the form of converging series, by an analytical iterative method using Fourier and Laplace transforms \cite{TT10,TT11}. There…
We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces
By employing the N-barrier method developed in the paper, we establish a new N-barrier maximum principle for diffusive Lotka-Volterra systems of two competing species. As an application of this maximum principle, we show under certain…
The nonlinear diffusion equation $u_t = (u^{- 4/3} u_x)_x$ is reduced by the substitution $u = v^{- 3/4}$ to an equation with quadratic nonlinearities possessing a polynomial invariant linear subspace of the maximal possible dimension equal…
This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful…
We investigate the long term behavior for a class of competition-diffusion systems of Lotka-Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system…
We prove existence and multiplicity of small amplitude periodic solutions of the completely resonant wave equation u_tt - u_xx + f(x,u)=0 with Dirichlet boundary conditions where f(x,u)=a_2 u^2 + a_3(x) u^3 + O(u^4) or f(x,u)= a_4 u^4 +…
We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion $$ \partial_tu+(-\Delta)^{1/2}\log(1+u)=0, $$ posed for $x\in \mathbb{R}$, with nonnegative initial data…
This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to the necessary conditions. In addition, convergence in distribution of positive…
We consider the semi linear Fisher-Kolmogorov-Petrovski-Piscounov equation for the advance of an advantageous gene in biology. Its non-smooth reaction function $f(u)$ allows for the introduction of travelling waves with a new profile. We…
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…