Monday, March 17, 2025 - 11:00 in V2-205
Variational Analysis of a Parametrized Family of Transmission Problems Coupling Nonlocal and Fractional Models
A talk in the Nonlocal Equations: Analysis and Numerics series by
Tadele Mengesha from Knoxville
| Abstract: |
I will present a work that examines the coupling of a model based on the regional fractional Laplacian and a nonlocal model employing a position-dependent interaction kernel. Both operators are inherently nonlocal and act on functions defined within their respective domains. The coupling occurs via a transmission condition across a hypersurface interface. The heterogeneous interaction kernel of the nonlocal operator leads to an energy space endowed with a well-defined trace operator. This, combined with well-established trace results of fractional Sobolev spaces, facilitates the imposition of a transmission condition across an interface. The family of problems will be parametrized by two key parameters that measure non-locality and differentiability. For each pair of parameters, we demonstrate existence of a solution to the resulting variational problems. Furthermore, we investigate the limiting behavior of these solutions as the parameters approach their extreme.
Within the CRC this talk is associated to the project(s): A7 |
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