A solution technique for random and nonlinear inverse heat conduction problems
type: Item
instance of: scholarly article
title: A solution technique for random and nonlinear inverse heat conduction problems
zbMATH Open document ID: 0746.65104
DOI: 10.1016/0378-4754(91)90023-V
published in: Mathematics and Computers in Simulation
publication date: 1992-06-25T00:00:00Z
review text: Inverse problems for the one-dimensional, inhomogeneous, nonlinear heat equation \(\partial_ tu(\omega,x,t)=\partial_ x(h(x,u(\omega,x,t))\partial_ xu(\omega,x,t))+ s(\omega,t)f(x)\) are considered in the interval \([0,1]\) (with a Neumann boundary condition at \(x=1\)). The source term \(f\) has compact support in (0,1) (\(h\) a known nonlinearity, \(s(\omega,t)\) random process, \(\omega\) random variable). The author proposes a `spatial' finite-element approach in conjunction with a Hermite expansion technique for the heat flux density to obtain a numerical procedure. The paper deals with two specific inverse questions: (1) reconstruction of temperature \(u(t,0)\) and its first derivative \(\partial_ xu(0,t)\); (2) reconstruction of the heat transfer coefficient \(H_ t\) occurring in the convective boundary condition \(h(0,u(0,t))\partial_ xu(0,t)=H_ t(\omega)(u(0,t)-T_ \infty(t))\), \(T_ \infty(t)\) a known ambient temperature, under the assumption that \(u\) is known at the initial time 0 as well as for all relevent times at a point \(x_ d\in [0,1]\) outside of the support of \(f\). The proposed procedure is supported by several numerical examples and graphs.
reviewed by: Rainer Picard
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 10055
zbMATH Keywords: Inverse problems
zbMATH Keywords: nonlinear heat equation
zbMATH Keywords: finite-element
zbMATH Keywords: Hermite expansion
zbMATH Keywords: reconstruction of temperature
zbMATH Keywords: reconstruction of the heat transfer coefficient
zbMATH Keywords: numerical examples
author: R. Riganti
MaRDI profile type: Publication
cites work: Q3771806
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description: scientific article; zbMATH DE number 10055