3 papers
math.AP2026
A Smoluchowski-Kramers approximation for the stochastic variational wave equation
Billel Guelmame, Julien Vovelle
We investigate the Smoluchowski-Kramers approximation for the one-dimensional periodic variational wave equation with state-dependent damping and additive noise. We show that weak…
math.AP2026
A quantitative averaging lemma for spatially dependent vector fields
Paul Alphonse, Billel Guelmame, Julien Vovelle
We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations ab…
math.AP2024
Global dissipative martingale solutions to the variational wave equation with stochastic forcing
Billel Guelmame, Julien Vovelle
We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existe…