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math.PR2022★ 1 cited
Synchronisation for scalar conservation laws via Dirichlet boundary
Ana Djurdjevac, Tommaso Rosati
We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not…
math.AP2022
The Allen-Cahn equation with generic initial datum
Martin Hairer, Khoa Lê, Tommaso Rosati
We consider the Allen-Cahn equation with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial cond…
math.PR2022
The wave speed of an FKPP equation with jumps via coordinated branching
Tommaso Rosati, András Tóbiás
We consider a Fisher-KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed given by $\…