Geodesic
Advection-diffusion equations with random coefficients on evolving hypersurfaces
Ana Djurdjevac1 orcid
1Freie Universität Berlin, Germany
Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 525-552

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DOI

We present the analysis of advection-diffusion equations with random coefficients on moving hypersurfaces. We define a weak and a strong material derivative, which account for the spatial movement. Then we define the solution space for these kind of equations, which is the Bochner-type space of random functions defined on a moving domain. We consider both cases, uniform and log-normal distributions of the diffusion coefficient. Under suitable regularity assumptions we prove the existence and uniqueness of weak solutions of the equation under analysis, and also we give some regularity results about the solution.
DOI : 10.4171/ifb/391
Classification : 35-XX, 00-XX
Mots-clés : Advection-diffusion, evolving surfaces, uncertainty quantification, random coefficients, existence

Ana Djurdjevac  1

1 Freie Universität Berlin, Germany 
Ana Djurdjevac. Advection-diffusion equations with random coefficients on evolving hypersurfaces. Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 525-552. doi: 10.4171/ifb/391
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     title = {Advection-diffusion equations with random coefficients on evolving hypersurfaces},
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     year = {2017},
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     number = {4},
     doi = {10.4171/ifb/391},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/391/}
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