RT Journal Article
T1 Partial mass concentration for fast-diffusions with non-local aggregation terms
A1 Carrillo, José A.
A1 Fernández-Jiménez, Alejandro
A1 Gómez-Castro, D.
AB We study well-posedness and long-time behaviour of aggregation-diffusion equations of the form ∂ρ∂t=Δρm+∇⋅(ρ(∇V+∇W∗ρ)) in the fast-diffusion range, 0<m<1, and V and W regular enough. We develop a well-posedness theory, first in the ball and then in Rd, and characterise the long-time asymptotics in the space W−1,1 for radial initial data. In the radial setting and for the mass equation, viscosity solutions are used to prove partial mass concentration asymptotically as t→∞, i.e. the limit as t→∞ is of the form αδ0+ρˆdx with α≥0 and ρˆ∈L1. Finally, we give instances of W≠0 showing that partial mass concentration does happen in infinite time, i.e. α>0.
YR 2023
FD 2023-04-11
LK https://hdl.handle.net/20.500.14352/73294
UL https://hdl.handle.net/20.500.14352/73294
LA eng
NO European Research Council Executive Agency (ERC)
NO Engineering and Physical Sciences Research Council (EPSRC)
NO Ministerio de Ciencia e Innovación
DS Docta Complutense
RD 10 abr 2025