Related papers: Eigenvalue asymptotics for the damped wave equatio…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the…
The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of…
We study eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$ of weighted random bipartite graphs $\Gamma= \Gamma_{N,p}$. We assume that the graphs have $N$ vertices, the ratio of parts is $\frac{\alpha}{1-\alpha}$ and the…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that depends…
A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved,…
A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0,…
This paper is concerned with the eigenvalues and linear inviscid damping of the 2D capillary gravity water waves of finite depth $x_2\in(-h,0)$ linearized at a monotone shear flow $U(x_2)$. Unlike the linearized Euler equation in a fixed…
In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of this work, in the presence of active scatterers, we present a systematic method to find arbitrary large-order zero…
We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear…
We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.
We propose a generalization of the asymptotic equipartition property to discrete sources with an ambiguous alphabet, and prove that it holds for irreducible stationary Markov sources with an arbitrary distinguishability relation. Our…
We investigate size Ramsey numbers involving bipartite graphs. It is proved that, if each forbidden graph is fixed or grows with n (in a certain uniform manner), then the extremal function has a linear asymptotics. The corresponding slope…
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that…