Determination of source parameter in parabolic equations

J. R. Cannon, Yanping Lin, Shingmin Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

106 Citations (Scopus)

Abstract

The authors consider the problem of finding u=u(x, t) and p=p(t) which satisfy u = Lu + p(t) + F(x, t, u, x, p(t)) in Q T=Ω×(0, T], u(x, 0)=ø(x), x∈Ω, u(x, t)=g(x, t) on ∂Ω×(0, T] and either ∫G(t) Φ(x,t)u(x,t)dx = E(t), 0 ≤ t ≤ T or u(x0, t)=E(t), 0≤t≤T, where Ω∋R n is a bounded domain with smooth boundary ∂Ω, x 0∈Ω, L is a linear elliptic operator, G(t)∋Ω, and F, ø, g, and E are known functions. For each of the two problems stated above, we demonstrate the existence, unicity and continuous dependence upon the data. Some considerations on the numerical solution for these two inverse problems are presented with examples.
Original languageEnglish
Pages (from-to)85-94
Number of pages10
JournalMeccanica
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Jun 1992
Externally publishedYes

Keywords

  • Inverse problem
  • Parabolic equations

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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