Thursday, March 9, 2023 - 11:40 in H2
Concentration limit for non-local dissipative convection-diffusion kernels on the hyperbolic space
A talk in the Nonlocal Equations: Analysis and Numerics 2023 series by
Dragos Manea from Bucharest
| Abstract: |
We study a non-local, non-linear convection-diffusion equation on the
hyperbolic space $\mathbb{H}^N$, governed by two kernels, one for each
of the diffusion and convection parts. One main novelty is the
constucion of the non-symmetric convection kernel defined on the tangent
bundle and invariant under the geodesic flow.
Next, we consider the relaxation of this model to a local problem, as
the kernels get concentrated near the origin of each tangent space.
Under some regularity and integrability conditions, we prove that the
solution of the concentrated non-local problem converges to that of the
local convection-diffusion equation.
We prove and then use in this sense a compactness tool on manifolds
inspired by the work of Bourgain-Brezis-Mironescu.
Within the CRC this talk is associated to the project(s): A7 |
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