相关论文: Fisher-KPP-type models of biological invasion: Ope…

We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…

In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents…

In this paper we present a method for estimating unknown parameter that appear in a two dimensional nonlinear reaction-diffusion model of cancer invasion. This model considers that tumor-induced alteration of microenvironmental pH provides…

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The…

A computational fluid model is developed to study waves and instabilities. A new technique involving initial perturbations in configuration space have been implemented to excite the plasma waves; i.e. the perturbations acting similar to a…

In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has become one of the most…

l flows and flat-plate boundary layers. However, it predicts too low a turbulent kinetic energy. This is a feature it shares with most other two-equation turbulence models. When comparing the terms in the k equations with DNS data it is…

This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…

We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convection-diffusion type problems: scalar advection-diffusion,…

We consider a Fisher-KPP equation with density-dependent diffusion and advection, arising from a chemotaxis-growth model. We study its behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We…

We study the long-time behavior of a triangular system of Fisher--KPP type with $k$ interacting components, associated with a reducible multitype branching Brownian motion with $k$ types of particles. For this cascading system, we prove…

Diffusion models have exhibited exciting capabilities in generating images and are also very promising for video creation. However, the inference speed of diffusion models is limited by the slow sampling process, restricting its use cases.…

Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm…

We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…

The notion of traveling wave, which typically refers to some particular spatio-temporal con- nections between two stationary states (typically, entire solutions keeping the same profile's shape through time), is essential in the…

Our investigation focuses on the asymptotic spreading behavior of the Fisher-KPP equation with a mixed local-nonlocal operator in the diffusion (see the work by X. Cabr\'e and J.-M. Roquejoffre, 2013, ref.[8]) to the setting of mixed…

In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < $\alpha$ < 1. We turn the free interface problem…

An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which…

The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…

We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its traveling waves. Specifically, we establish…