178 citations · 981 across the 75 of their papers we have counts for
12 papers · 1 filter
Diffusion bounds for non-autonomous degenerate parabolic equations
Marius Lemm, Israel Michael Sigal, Jingxuan Zhang
We consider possibly degenerate non-autonomous parabolic equations in spaces for all , and prove Gaussian space-time upper bounds of the Davies-Gaffney, or i…
The FitzHugh-Nagumo system on undulated cylinders: spontaneous symmetrization and effective system
Georgia Karali, Konstantinos Tzirakis, Israel Michael Sigal
We consider the FitzHugh-Nagumo system on undulated cylindrical surfaces modeling nerve axons. We show that for sufficiently small radii and for initial conditions close to radiall…
Maximal Speed of Quantum Propagation for the Hartree equation
Jack Arbunich, Jérémy Faupin, Fabio Pusateri +1
We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on th…
Ginzburg-Landau Equations on Non-compact Riemann Surfaces
Nicolas M. Ercolani, Israel Michael Sigal, Jingxuan Zhang
We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less…
Near-Pulse Solutions of the FitzHugh-Nagumo Equations on Cylindrical Surfaces
Afroditi Talidou, Almut Burchard, Israel Michael Sigal
We introduce a geometrical extension of the FitzHugh-Nagumo equations describing propagation of electrical impulses in nerve axons. In this extension, the axon is modeled as a warp…
Long-time behaviour of time-dependent density functional theory
Fabio Pusateri, Israel Michael Sigal
The density functional theory (DFT) is a remarkably successful theory of electronic structure of matter. At the foundation of this theory lies the Kohn-Sham (KS) equation. In this…
Ginzburg-Landau equations on Riemann surfaces of higher genus
D. Chouchkov, N. M. Ercolani, S. Rayan +1
We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary genus. In particular: - we construct explicitly the (local moduli space of gauge-equivalent) solutions in a…
On Blowup in Nonlinear Heat Equations
D. Egli, Z. Gang, W. Kong +1
We establish the asymptotics of blowup for nonlinear heat equations with superlinear power nonlinearities in arbitrary dimensions and we estimate the remainders.
Neck Pinching Dynamics Under Mean Curvature Flow
Zhou Gang, Israel Michael Sigal
In this paper we study motion of surfaces of revolution under the mean curvature flow. For an open set of initial conditions close to cylindrical surfaces we show that the solution…
Blow-up in Nonlinear Heat Equations
S. Dejak, Zhou Gang, I. M. Sigal +1
We study the blow-up problem of one-dimensional nonlinear heat equations. Our result shows that for a certain class of initial conditions, the solutions blow up in finite time and…
Effective Dynamics of Magnetic Vortices
S. Gustafson, I. M. Sigal
We study solutions of Ginzburg-Landau-type evolution equations (both dissipative and Hamiltonian) with initial data representing collections of widely-spaced vortices. We show that…
The Stability of Magnetic Vortices
S. Gustafson, I. M. Sigal
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for…