Local and non-local boundary quenching

Catherine A. Roberts, W. E. Olmstead

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The quenching problem is examined for a one-dimensional heat equation with a non-linear boundary condition that is of either local or non-local type. Sufficient conditions are derived that establish both quenching and non-quenching behaviour. The growth rate of the solution near quenching is also given for a power-law non-linearity. The analysis is conducted in the context of a nonlinear Volterra integral equation that is equivalent to the initial-boundary value problem.

Original languageEnglish (US)
Pages (from-to)1465-1484
Number of pages20
JournalMathematical Methods in the Applied Sciences
Issue number16
StatePublished - Nov 10 1999

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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