Related papers: Bistable reaction-diffusion on a network
In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
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…
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of…
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. The solutions are assumed to be localized in the past. Under certain…
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…
Reaction-diffusion equations are widely used to describe a variety of phenomena such as pattern formation and front propagation in biological, chemical and physical systems. In the one-dimensional model with a balanced bistable reaction…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
Reaction-diffusion equations on infinite graphs can have an infinite number of stationary solutions. These solutions are generally described as roots of a countable system of algebraic equations. As a generalization of periodic stationary…
We consider a general form of reaction-dispersion equations with non-local dispersal and local reaction. Under some general conditions, we prove the non-existence of transition fronts, as well as some stretching properties at large time for…
Multiple time scales problems are investigated by combining geometrical and analytical approaches. More precisely, for fast-slow reaction-diffusion systems, we first prove the existence of slow manifolds for the abstract problem under the…
The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the…
In this paper we provide explicit description of the pinning region and propagation reversal phenomenon for the bistable reaction diffusion equation on regular biinfinite trees. In contrast to the general existence results for smooth…
We prove the existence and we study the stability of the kink-like fixed points in a simple Coupled Map Lattice for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value…
We study the existence of monotone wavefronts for a general family of bistable reaction-diffusion equations with delayed reaction term $g$. Differently from previous works, we do not assume the monotonicity of $g(u,v)$ with respect to the…
We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation…