A parabolic equation on domains with random boundaries

Published 29 Sep 2020 in math.AP, cs.NA, and math.NA | (2009.13997v1)

Abstract: A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented. Boundary integral equation methods are used to compute statistical moments of the shape derivative.

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