7 citations · 14 across the 8 of their papers we have counts for
10 papers
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…
Solutions of abstract wave equations, eigenvalues and resonances
Yuri Latushkin, Alin Pogan
We prove general representation formulas for strongly continuous cosine and sine operator families in terms of scattering resonances of their generators. This generalizes known res…
Resonances for the one dimensional Schrödinger operator with the matrix-valued complex square-well potential
Yuri Latushkin, Alin Pogan
We study the resonances of (generally, non-selfadjoint) Schrödinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex…
Uniform bounds of families of analytic semigroups and Lyapunov linear stability of planar fronts
Yuri Latushkin, Alin Pogan
We study families of analytic semigroups, acting in a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parame…
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…
Reverse norms and L infinity exponential decay for a class of degenerate evolution systems arising in kinetic theory
Alin Pogan, Kevin Zumbrun
We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann an…
Center manifolds for a class of degenerate evolution equations and existence of small amplitude kinetic shocks
Alin Pogan, Kevin Zumbrun
We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existenc…
Stable manifolds for a class of degenerate evolution equations and exponential decay of kinetic shocks
Alin Pogan, Kevin Zumbrun
We construct stable manifolds for a class of degenerate evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kin…
O(2) Hopf bifurcation of viscous shock waves in a channel
Alin Pogan, Jinghua Yao, Kevin Zumbrun
Extending work of Texier and Zumbrun in the semilinear non-re ection symmetric case, we study O(2) transverse Hopf bifurcation, or \cellular instability," of viscous shock waves in…
Quasi-gradient systems, modulational dichotomies, and stability of spatially periodic patterns
Alin Pogan, Arnd Scheel, Kevin Zumbrun
Extending the approach of Grillakis-Shatah-Strauss, Bronski-Johnson-Kapitula, and others for Hamiltonian systems, we explore relations between the constrained variational problem $…