相关论文: The mathematical theory of splitting-merging patte…

We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as…

We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the…

We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…

A new type of wave-mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a…

We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are…

We study extremal shocks of $1$-d hyperbolic systems of conservation laws which fail to be genuinely nonlinear. More specifically, we consider either $1$- or $n$-shocks in characteristic fields which are either concave-convex or…

Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…

We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…

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…

For models describing water waves, Constantin and Escher's works have long been considered as the cornerstone method for proving wave breaking phenomena. Their rigorous analytic proof shows that if the lowest slope of flows can be…

We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…

Non-Hermiticity and dephasing, collaborating in an unusual wave packet dynamics, realizes unconventional entanglement evolution in a disordered, interacting and asymmetric (non-reciprocal) quantum medium. Taking the Hatano-Nelson model as a…

We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…

We identify a new universality class of phase transitions that arises in non-normal systems, challenging the classical view that transitions require eigenvalue instabilities. In traditional bifurcation theory, critical phenomena emerge when…

The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account,…

In this paper, we consider some hyperbolic variants of the mass conserving Allen-Cahn equation, which is a nonlocal reaction-diffusion equation, introduced (as a simpler alternative to the Cahn-Hilliard equation) to describe phase…

Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we can consider the class of weak solutions containing shock waves depending upon some small scale parameters. In this…

Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…

This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…

We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…