3 papers
math.AP2026
From a Scalar Parabolic Oscillator to Topological Thermostats: Selective Feeback Control of Harmonic Flow Modes
Sandro Merino
This paper develops a Hodge-theoretic feedback framework for flow-valued states, motivated by scalar parabolic thermostat problems with localized sensors and dual sources. On a con…
math.AP2020
On Wiener's Violent Oscillations, Popov's curves and Hopf's Supercritical Bifurcation for a Scalar Heat Equation
Patrick Guidotti, Sandro Merino
A parameter dependent perturbation of the spectrum of the scalar Laplacian is studied for a class of nonlocal and non-self-adjoint rank one perturbations. A detailed description of…
math.AP2019
On the Maximal Parameter Range of Global Stability for a Nonlocal Thermostat Model
Patrick Guidotti, Sandro Merino
The global asymptotic stability of the unique steady state of a nonlinear scalar parabolic equation with a nonlocal boundary condition is studied. The equation describes the evolut…