64 citations · 219 across the 45 of their papers we have counts for
11 papers · 1 filter
The Damped Waves Equation and generalized Cosine and Sine families on Banach spaces
Yuri Latushkin, Alin Pogan
We study the abstract damped wave equation on a Banach space, allowing the damping coefficient to be unbounded. By recasting the equation as a first-order system and identifying co…
The essential spectrum of periodically-stationary solutions of the complex Ginzburg-Landau equation
John Zweck, Yuri Latushkin, Jeremy L. Marzuola +1
We establish the existence and regularity properties of a monodromy operator for the linearization of the cubic-quintic complex Ginzburg-Landau equation about a periodically-statio…
Exponential dichotomies for elliptic PDE on radial domains
Margaret Beck, Graham Cox, Christopher Jones +2
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one…
A dynamical approach to semilinear elliptic equations
Margaret Beck, Graham Cox, Christopher Jones +2
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in is given in terms of an infinite-dimensional dynamical system.…
Eigenvalues of the linearized 2D Euler equations via Birman-Schwinger and Lin's operators
Yuri Latushkin, Shibi Vasudevan
We study spectral instability of steady states to the linearized 2D Euler equations on the torus written in vorticity form via certain Birman-Schwinger type operators and…
Spectrum of non-planar traveling waves
Anna Ghazaryan, Yuri Latushkin, Alin Pogan
In this paper we prove that a class of non self-adjoint second order differential operators acting in cylinders have only real discrete s…
Stability of a planar front in a multidimensional reaction-diffusion system
Anna Ghazaryan, Yuri Latushkin, Xinyao Yang
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the directi…
The Maslov Index and the Spectra of Second Order Elliptic Operators
Yuri Latushkin, Selim Sukhtaiev
We consider second order elliptic differential operators on a bounded Lipschitz domain . Firstly, we establish a natural one-to-one correspondence between their self-adjoint ext…
The Morse and Maslov Indices for Schrödinger Operators
Yuri Latushkin, Alim Sukhtayev, Selim Sukhtaiev
We study the spectrum of Schrödinger operators with matrix valued potentials utilizing tools from infinite dimensional symplectic geometry. Using the spaces of abstract boundary va…
Derivatives of (Modified) Fredholm Determinants and Stability of Standing and Traveling Waves
Fritz Gesztesy, Yuri Latushkin, Kevin Zumbrun
Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman-Schwinger type integr…
The Spectrum of a linearized 2D Euler operator
Y. Latushkin, Y. Li, M. Stanislavova
We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two dimensional fluid at a steady state with the vorticity…