Related papers: Minimum wave speeds in monostable reaction-diffusi…
The analytical theory of diffusive cosmic ray acceleration at parallel stationary shock waves with magnetostatic turbulence is generalized to arbitrary shock speeds $V_s=\beta_1c$, including in particular relativistic speeds. This is…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories.…
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…
We consider the compressible Navier-Stokes equations for isentropic dynamics with real viscosity on a bounded interval. In the case of boundary data defining an admissible shock wave for the corresponding unviscous hyperbolic system, we…
We discuss a class of hyperbolic reaction-diffusion equations and apply the modified method of simplest equation in order to obtain an exact solution of an equation of this class (namely the equation that contains polynomial nonlinearity of…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
Molecular collisions can be studied at very low relative kinetic energies, in the milliKelvin range, by merging codirectional beams with much higher translational energies, extending even to the kiloKelvin range, provided that the beam…
We give a complete characterization of the boundary traces $\varphi_i$ ($i=1,\dots,K$) supporting spiraling waves, rotating with a given angular speed $\omega$, which appear as singular limits of competition-diffusion systems of the type \[…
We study dynamical properties of the cubic lowest Landau level equation, which is used in the modeling of fast rotating Bose-Einstein condensates. We obtain bounds on the decay of general stationary solutions. We then provide a…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
Reaction-Diffusion equations can present solutions in the form of traveling waves. Such solutions evolve in different spatial and temporal scales and it is desired to construct numerical methods that can adopt a spatial refinement at…
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…
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a…
Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such constructed upper and lower…
Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to…
In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with H\"older continuous paths, covering in particular fractional Brownian…
We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by…
Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian…