The one-dimensional heat equation with a nonlocal initial condition

W. E. Olmstead*, C. A. Roberts

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A boundary value problem for the one-dimensional heat equation is considered under the constraint of a nonlocal initial condition. The problem is investigated by conversion to a Fredholm integral equation. The solution of the integral equation is derived as an eigenfunction expansion that is valid for situations in which either uniqueness or nonuniqueness applies. Circumstances under which a resonance effect occurs are discussed and illustrated with an example.

Original languageEnglish (US)
Pages (from-to)89-94
Number of pages6
JournalApplied Mathematics Letters
Issue number3
StatePublished - May 1997

ASJC Scopus subject areas

  • Applied Mathematics

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