相关论文: Burgers' equation revisited: extension of mono-dim…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…
This paper studies the 1D pressureless turbulence (the Burgers equation). It shows that reliable numerics in this problem is very easy to produce if one properly discretizes the Burgers equation. The numerics it presents confirms the 7/2…
We study the stability of traveling wave solutions to the Burgers--Hilbert equation on $\mathbb{T}$ in the regime of small frequency $\omega$ and large wave speed $c$. For $\omega = 3$ and $c \approx 1.1$, we show that the linearized…
We prove the existence and uniqueness of a classical solution to a multidimensional non-potential stochastic Burgers equation with H\"older continuous initial data. Our motivation is the adhesion model in the theory of formation of the…
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well…
We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these subcomplexes capture many important structural properties of…
Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the…
The one dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed…
Motivated by the theory of spin-glasses in physics, we study the so-called reconstruction problem for the related distributions on the tree, and on the sparse random graph $G(n,d/n)$. Both cases, reduce naturally to studying broadcasting…
We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schr\"{o}dinger boundary data problem for the random matter transport. This entails…
We investigate the Kazdan-Warner equation on a network. In this case, the differential equation is defined on each edge, while appropriate transition conditions of Kirchhoff type are prescribed at the vertices. We show that the…
The paper recalls two of the regularity results for Burgers' equation, and discusses what happens in the case of genuinely nonlinear, strictly hyperbolic systems of conservation laws. The first regularity result which is considered is…
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…
Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler…
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on…