相关论文: Shock selection in reaction--diffusion equations w…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
We revisit the diffusive instability in dusty disks that arises when the dust mass diffusivity and/or viscosity decreases sufficiently steeply with increasing dust density. Our updated model includes an incompressible, viscous gas that…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
In the long-wave regime, nonlinear waves may undergo a phase transition from a smooth to a fast oscillatory behaviour. We study this phenomenon, commonly known as dispersive shock, in the light of Dubrovin's universality conjecture , and we…
Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham…
The analysis of surface wave dispersion curves is a way to infer the vertical distribution of shear-wave velocity. The range of applicability is extremely wide going, for example, from seismological studies to geotechnical characterizations…
Collisionless shocks are often studied in two spatial dimensions (2D), to gain insights into the 3D case. We analyze diffusive shock acceleration for an arbitrary number $N\in\mathbb{N}$ of dimensions. For a non-relativistic shock of…
Astrophysical explosions are accompanied by the propagation of a shock wave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity $V$ can be non-relativistic ($V \ll c$, where $c$ is the…
The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
We study numerically and experimentally the impact of temporal randomness on the formation of analogue optical blast-waves in nonlinear fiber optics. The principle-of-operation is based on a two-components nonlinear interaction occurring…
We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
We demonstrate the controllable generation of distinct types of dispersive shock-waves emerging in a quantum droplet bearing environment with the aid of step-like initial conditions. Dispersive regularization of the ensuing hydrodynamic…
The defocusing nonlinear Schr\"odinger (NLS) equation is studied for a family of step-like initial data with piecewise constant amplitude and phase velocity with a single jump discontinuity at the origin. Riemann-Hilbert and steepest…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
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…
We study a family of reaction-diffusion equations that present a doubly nonlinear character given by a combination of the $p$-Laplacian and the porous medium operators. We consider the so-called slow diffusion regime, corresponding to a…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…