Related papers: A free boundary problem for spreading under shifti…
This paper is concerned with the speeds of propagation for the monostable Lotka-Volterra competition-diffusion system in general unbounded domains of $\mathbb{R}^N$. We first establish various definitions of spreading speeds at large time…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
This is the third part of our series of work devoted to the dynamics of an epidemic model with nonlocal diffusions and free boundary. This part is concerned with the rate of accelerated spreading for three types of kernel functions when…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
In numerous contexts, individuals may decide whether they take actions to mitigate the spread of disease, or not. Mitigating the spread of disease requires an individual to change their routine behaviours to benefit others, resulting in a…
We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…
We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. A couple of decades ago, it was observed experimentally that the penetration depth versus…
Fitness consequence of dispersal depends on property of the entire landscape, which patches are available and what are the cost of moving. These are information that are not available locally when an organism make the decision to disperse.…
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
We study a translational invariant free fermions model in imaginary time, with nearest neighbor and next-nearest neighbor hopping terms, for a class of inhomogeneous boundary conditions. This model is known to give rise to limit shapes and…
We consider an individual-based two-dimensional spatial model with nearest-neighbor preemptive competition to study front propagation between an invader and a resident species. In particular, we investigate the asymptotic front velocity and…
In this paper, we study the stability of traveling wave solutions arising from a credit rating migration problem with a free boundary, After some transformations, we turn the Free Boundary Problem into a fully nonlinear parabolic problem on…
In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the…