6 papers · 1 filter
Optimal stability estimates and a new uniqueness result for advection-diffusion equations
Víctor Navarro-Fernández, André Schlichting, Christian Seis
This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev reg…
Oscillations in a Becker-Döring model with injection and depletion
Barbara Niethammer, Robert L. Pego, André Schlichting +1
We study the Becker-Döring bubblelator, a variant of the Becker-Döring coagulation-fragmentation system that models the growth of clusters by gain or loss of monomers. Motivated by…
Self-similar behavior of the exchange-driven growth model with product kernel
Constantin Eichenberg, André Schlichting
We study the self-similar behavior of the exchange-driven growth model, which describes a process in which pairs of clusters, consisting of an integer number of monomers, interact…
Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
Antonio Esposito, Francesco S. Patacchini, André Schlichting +1
We consider dynamics driven by interaction energies on graphs. We introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with…
Barriers of the McKean--Vlasov energy via a mountain pass theorem in the space of probability measures
Rishabh S. Gvalani, André Schlichting
We show that the empirical process associated with a system of weakly interacting diffusion processes exhibits a form of noise-induced metastability. The result is based on an anal…
Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus
J. A. Carrillo, R. S. Gvalani, G. A. Pavliotis +1
We study the McKean-Vlasov equation \[ \partial_t \varrho= β^{-1} Δ\varrho + κ\nabla \cdot (\varrho \nabla (W \star \varrho)) \, , \] with periodic boundary conditions on the torus…