相关论文: KPP reaction-diffusion systems with loss inside a …
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…
We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…
We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a "thin-front limit," we are able to deduce a Hamilton-Jacobi equation with a suitable effective Hamiltonian on the road…
We study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by further developing the method based on the theory of viscosity solutions of…
We consider an optimal insulation problem of a given domain in $\mathbb R^N$. We study a model of heat trasfer determined by convection; this corresponds, before insulation, to a Robin boundary value problem. We deal with a prototype which…
In this paper we apply the differential inequality technique of Payne {\it et. al} \cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set…
We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to…
In this paper, we extend and complement previous works about propagation in kinetic reaction-transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction…
This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…
In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit as k tends to infinithy,spatial segregation results in…
This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…
In this paper, we consider a drift-diffusion system describing the corrosion of an iron based alloy in a nuclear waste repository. In comparison with the classical drift-diffusion system arising in the modeling of semiconductor devices, the…
In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: $\delta_tu = J \times u - u + f (x, u) t \in R^+, x \in R^N$, where J is a probability density and f is a KPP nonlinearity…
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy…