Related papers: Singular limits for models of selection and mutati…
We are concerned with the well-posedness of Neumann boundary value problems for nonlocal Hamilton-Jacobi equations related to jump processes in general smooth domains. We consider a nonlocal diffusive term of censored type of order less…
In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
We consider a generalization of the Lotka-McKendrick problem describing the dynamics of an age-structured population with time-dependent vital rates. The generalization consists in allowing the initial and the boundary conditions to be…
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness…
We study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour in the large…
We study unbounded (viscosity) supersolutions of the Evolutionary p-Laplace Equation in the slow diffusion case. The supersolutions fall into two widely different classes, depending on whether they are locally summable to the power p-2 or…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
We study the asymptotic behavior of the principal eigenvalue of a weakly coupled, cooperative linear elliptic system in a stationary ergodic heterogeneous medium. The system arises as the so-called multigroup diffusion model for neutron…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
By means of a particle model that includes interactions only via the local particle concentration, we show that hyperballistic diffusion may result. This is done by findng the exact solution of the corresponding non-linear diffusion…
We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators. Our main results is a stochastic representation of…
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…