Related papers: Numerical Solutions to Singular Reaction-Diffusion…
Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…
The reaction-diffusion equation is one of the cornerstones equations in applied science and engineering. In the present study, a deep neural network has been trained in order to predict the solution of the equation with different…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
We consider a family of exact solutions to a nonlinear reaction-diffusion model, constructed using nonclassical symmetry analysis. In a particular limit, the mathematical model approaches the well-known Fisher-KPP model, which means that it…
For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations (associated with the Dirichlet forms) starting from all…
Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. Excluded volume effects are taken into account in the thermodynamically self-consistent way. The model exhibits a 1-st order phase…
We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…
Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good understanding of the vanishing order and size of singular and zero…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
The statistical model of Chase and Mekjian, which offers an analytic solution for the canonical ensemble of non-interacting fragments, is investigated for it's thermodynamic behavior. Various properties of the model, which exhibits a…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…