Related papers: Minimum wave speeds in monostable reaction-diffusi…
This paper is concerned with the large-time dynamics of bounded solutions of reaction-diffusion equations with bounded or unbounded initial support in R N. We start with a survey of some old and recent results on the spreading speeds of the…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
In this paper, extending previous results of \cite{J1}, we obtain pointwise nonlinear stability of periodic traveling reaction-diffusion waves, assuming spectral linearized stability, under nonlocalized perturbations. More precisely, we…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system…
We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in…
Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a…
Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
A geometrically invariant concept of fast-slow vector fields perturbed by transport terms (describing molecular diffusion processes) is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields to…
The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
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…
We present here a semi-analytical solution of the problem of particle acceleration at non-linear shock waves with a free escape boundary at some location upstream. This solution, besides allowing us to determine the spectrum of particles…
We consider equation $u_t(t,x) = \Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*) $, when $g:\R_+\to \R_+$ has exactly two fixed points: $x_1= 0$ and $x_2=\kappa>0$. Assuming that $g$ is unimodal and has negative Schwarzian, we indicate explicitly a…
Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…