English
Related papers

Related papers: Is single-mode lasing possible in an infinite peri…

200 papers

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…

Optimization and Control · Mathematics 2014-10-01 Christophe Prieur , Antoine Girard , Emmanuel Witrant

We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite…

Analysis of PDEs · Mathematics 2020-05-15 Huaian Diao , Hongyu Liu , Long Zhang , Jun Zou

We consider the plasma confined in a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, and look at a certain class of equilibria, assuming axisymmetry in the problem. We prove a sharp…

Analysis of PDEs · Mathematics 2019-10-15 Katherine Zhiyuan Zhang

Fluid instabilities arise in a variety of contexts and are often unwanted results of engineering imperfections. In one particular model for a magnetized target fusion reactor, a pressure wave is propagated in a cylindrical annulus comprised…

Fluid Dynamics · Physics 2017-04-26 Michael Lindstrom

We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…

Analysis of PDEs · Mathematics 2018-10-09 Andrii Anikushyn , Michael Pokojovy

We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…

Dynamical Systems · Mathematics 2022-08-29 Sachin Bhalekar , Prashant M. Gade , Divya Joshi

The effect of rotation upon the classical two-layer Rayleigh-Taylor instability is considered theoretically and compared with previous experimental results. In particular we consider a two-layer system with an axis of rotation that is…

Fluid Dynamics · Physics 2016-03-03 Matthew M. Scase , Kyle A. Baldwin , Richard J. A. Hill

This work studies the stabilization for a periodic parabolic system under perturbations in the system conductivity. A perturbed system does not have any periodic solution in general. However, we will prove that the perturbed system can…

Optimization and Control · Mathematics 2009-02-26 Ling Lei

For flowing quantum gases, it has been found that at long times an initial black-hole laser (BHL) configuration exhibits only two possible states: the ground state or a periodic self-oscillating state of continuous emission of solitons. So…

General Relativity and Quantum Cosmology · Physics 2021-03-03 J. R. M. de Nova , P. F. Palacios , I. Carusotto , F. Sols

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

Analysis of PDEs · Mathematics 2018-08-15 Yue-Hong Feng , Xin Li , Shu Wang

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…

Analysis of PDEs · Mathematics 2018-01-17 Blake Barker , Soyeun Jung , Kevin Zumbrun

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Dynamical Systems · Mathematics 2016-12-14 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

We study the orbital stability and instability of single-spike bound states of semiclassical nonlinear Schrodinger (NLS) equations with critical exponent, linear and nonlinear optical lattices (OLs). These equations may model…

Analysis of PDEs · Mathematics 2010-06-25 Tai-Chia Lin , Juncheng Wei , Wei Yao

We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g. a bad-cavity correction to the Henry…

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…

Optimization and Control · Mathematics 2019-10-04 Masashi Wakaiki , Yutaka Yamamoto

We prove the stability of $L^{1}$ self-similar profiles under the hard-to-Maxwell potential limit for the one-dimensional inelastic Boltzmann equation with moderately hard potentials which, in turn, leads to the uniqueness of such profiles…

Analysis of PDEs · Mathematics 2024-08-09 R. Alonso , V. Bagland , J. A. Cañizo , B. Lods , S. Throm

Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and…

Numerical Analysis · Mathematics 2025-03-12 S. A. Hosseini , I. V. Karlin

We report the first experimental observation of multi-stable states in a single-longitudinal mode semiconductor ring laser. We show how the operation of the device can be steered to either monostable, bistable or multi-stable dynamical…

We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is…

This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…

Analysis of PDEs · Mathematics 2023-06-01 Harsha Hutridurga , Krishan Kumar , Amiya K. Pani