23 citations · 80 across the 43 of their papers we have counts for
53 papers
On the derivative loss for a class of abstract evolution equations with time dependent oscillating coefficients vanishing at initial time
Marina Ghisi, Massimo Gobbino, Michael Reissig
We consider an abstract wave-type evolution equation with a propagation speed depending only on time. We assume that this propagation speed is the product of a monotone, but possib…
Billiards, Refraction, and Blow-Up for Kirchhoff Equations
Marina Ghisi, Massimo Gobbino
We start from a simple problem in geometric optics. A particle moves between two homothetic ellipses, with refraction at the inner interface and reflection at the outer one. In a s…
Fifty Years of Wave Equations with Time-Dependent Propagation Speeds: A Variational Perspective and New Frontiers
Marina Ghisi, Massimo Gobbino
We study abstract wave equations with time-dependent propagation speed under strict hyperbolicity. Our starting point is the observation that a substantial part of the classical en…
The model example of wave equation with oscillating scale-invariant damping
Marina Ghisi, Massimo Gobbino
We analyze a simple example of wave equation with a time-dependent damping term, whose coefficient decays at infinity at the scale-invariant rate and includes an oscillatory compon…
Generalized energy conservation for linear wave equations with time-dependent propagation speed
Marina Ghisi, Massimo Gobbino
We consider a wave equation with a time-dependent propagation speed, whose potential oscillations are controlled through bounds on its first and second derivatives and by limiting…
Resonance effects for linear wave equations with scale invariant oscillating damping
Marina Ghisi, Massimo Gobbino
We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case.…