We consider the Fisher–KPP equation with a non-local saturation effect defined through an interaction kernel ϕ(x) and investigate possible differences standard equation. Our first concern is existence of steady states. prove that if Fourier transform positive or length σ short enough, then only states are u ≡ 0 1. Next, we study travelling waves. this admits wave solutions connect = to unknown state u∞(x), for all speeds c ⩾ c*. The connects u∞(x) 1 under aforementioned conditions:...

In this monograph, we review the theory and establish new general results regarding spreading properties for heterogeneous reaction-diffusion equations: <disp-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="partial-differential Subscript t Baseline u minus sigma-summation Underscript i comma j equals 1 Overscript upper N Endscripts a left-parenthesis x right-parenthesis partial-differential q f period"> <mml:semantics> <mml:mrow>...

We consider the traveling wave problem for one dimensional Keller-Segel system with a birth term of either Fisher/KPP type or truncation small population densities. prove that there exists solution under some stability conditions on coefficients which enforce an upper bound and \dot H^1(\R) estimates. Solutions in KPP case are built as limit waves truncated rates (similar to ignition temperature combustion theory). also discuss general bounds long time convergence Cauchy particular linear...

We study existence and nonexistence results for generalized transition wave solutions of space-time heterogeneous Fisher-KPP equations.When the coefficients equation are periodic in space but otherwise depend a fairly general fashion on time, we prove that such waves exist as soon their speed is sufficiently large sense.When this too small, do not anymore; result holds without assuming periodicity space.These necessary sufficient conditions proved to be optimal when both time.Our method...

Our interest here is to find the invader in a two species, diffusive and competitive Lotka–Volterra system particular case of travelling wave solutions. We investigate role diffusion homogeneous domains. might expect priori different cases: strong interspecific competition weak competition. In this paper, we study first one obtain clear conclusion: invading species is, up fixed multiplicative constant, more one.

The goal of this paper is to provide a qualitative analysis the optimisation space-time periodic principal eigenvalues. Namely, considering fixed time horizon $T$ and $d$-dimensional torus $\mathbb{T}^d$, let, for any $m\in L^\infty((0,T)\times\mathbb{T}^d)$, $\lambda(m)$ be eigenvalue operator $\partial_t-\Delta-m$ endowed with (time-space) boundary conditions. main question we set out answer following: how choose $m$ so as minimise $\lambda(m)$? This stems from population dynamics. We...

This paper is concerned with the study of large-time behavior solutions u a class one-dimensional reaction–diffusion equations monostable reaction terms f, including in particular classical Fisher-KPP nonlinearities. The nonnegative initial data 0(x) are chiefly assumed to be exponentially bounded as x tends + ∞ and separated away from unstable steady state 0 − ∞. On one hand, we give some conditions on which guarantee that, for λ > 0, quantity c = +f′(0)/λ asymptotic spreading speed, sense...

Traveling waves for the nonlocal Fisher Equation can exhibit much more complex behaviour than usual equation. A striking numerical observation is that a traveling wave with minimal speed connect dynamically unstable steady state 0 to Turing 1, see [12]. This proved in [1, 6] case where far from minimal, we expect be monotone.

Duration of post-vaccination protection against COVID-19 in nursing home (NH) residents is a critical issue. The objective this study was to estimate the duration IgG(S) response mRNA BNT162b2 vaccine NH with (COV-Yes) or without (COV-No) history SARS-CoV-2 infection.A 574 COV-Yes and COV-No were included 2 cohorts: Main (n = 115, median age 87 years) Confirmatory 459, 89 years). quantification carried out at three different time points following vaccine: (1st) seven (2nd) months after 2nd...

This paper is concerned with the periodic principal eigenvalue $k_\lambda(\mu)$ associated operator $-\frac{d^2}{dx^2}-2\lambda\frac{d}{dx}-\mu(x)-\lambda^2$, where $\lambda\in\mathbb{R}$ and $\mu$ continuous in $x\in\mathbb{R}$. Our main result that $k_\lambda(\mu^*)\leq k_\lambda(\mu)$, $\mu^*$ Schwarz rearrangement of function $\mu$. From a population dynamics point view, using reaction-diffusion modeling, this means fragmentation habitat an invading slows down invasion. We prove property...

We establish in this article spreading properties for the solutions of equations type $\partial$ t u -- a(x)$\partial$ xx q(x)$\partial$ x = f (x, u), where a, q, are only assumed to be uniformly continuous and bounded x, nonlinearity is monostable KPP between two steady states 0 1 initial datum compactly sup-ported. Using homogenization techniques, we construct speeds w $\le$ such that lim t$\rightarrow$+$\infty$ sup 0$\le$x$\le$wt |u(t, x)--1| all $\in$ (0, w) x$\ge$wt x)| \textgreater{}...

In this work we study the behaviour of travelling wave solutions for diffusive Hutchinson equation with time delay. Using a phase plane analysis prove existence solution each speed c⩾2. We show that given and admissible speed, such converge to unique maximal wavetrain. As consequence nontrivial wavetrain is equivalent non-converging stationary state u=1.

.Some pests and vectors of many vector-borne diseases (like mosquitoes for malaria dengue) are known to invade any homogeneous favorable territory, following a traveling wave type dynamic. The density individuals in the field is commonly modeled as solution bistable reaction-diffusion equation on an unbounded domain. In this work, we interested finding optimal strategy block such by means population elimination action prescribed subdomain (modeling, instance, effect mechanical or insecticide...