A parabolic equation on domains with random boundaries

2020/09/29 by Duong Thanh Pham, Thanh Tran, Pham, Duong Thanh +1
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.AP #math.NA

paper · pdf · doi:10.48550/arxiv.2009.13997

arxiv created 2020/09/29 · arxiv updated 2020/09/30

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.

Related

• Probabilistic representation of weak solutions to a parabolic boundary value problem on a non-smooth domain
• A shape calculus based method for a transmission problem with random interface
• Linear Parabolic Problems in Random Moving Domains
• Stochastic Cauchy Initial Value Formulation Of The Heat Equation For Random Field Initial Data: Smoothing, Harnack-Type Bounds And p-Moments
• A Probabilistic Approach to Shape Derivatives