Related papers: Diffusion-convection reaction equations with sign-…
We prove the existence and uniqueness of a traveling front and of its speed for the homogeneous heat equation in the half-plane with a Neumann boundary reaction term of non-balanced bistable type or of combustion type. We also establish the…
In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
Refraction of obliquely incident plane waves due to the interface of a vacuous half-space and a half-space occupied by a simply moving, nondissipative, isotropic dielectric-magnetic medium is considered, when the medium's velocity lies…
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…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
We study finite-time singularities in the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact…
We formulate the theory for a self-propelled domain in an excitable reaction-diffusion system in two dimensions where the domain deforms from a circular shape when the propagation velocity is increased. In the singular limit where the width…
Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. In natural doubly diffusive convection, the gradients of…
We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions…
This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…
Bifurcation properties, stability behavior, dynamics, and the heat transfer of convection structures in a horizontal fluid layer that is driven away from thermal equilibrium by imposing a vertical temperature difference are compared with…
We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter…
This article provides techniques of raising the regularity of fractional order equations and resolves fundamental questions on the one-dimensional homogeneous boundary-value problem of skewed (double-sided) fractional diffusion advection…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front…
The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints, which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane…