Stationary solutions of an equation modelling ohmic heating

Pedro Frettas, M. Grinfeld

Research output: Contribution to journalArticle

Abstract

In this note, we study questions of multiplicity and stability of stationary solutions of the nonlocal reaction-diffusion equation ut = uxx+?f{hook}(u) a + sh{phonetic} 0 1f{hook}(u)dx2 which arises in the theory of electrical devices with temperature-dependent resistivity and where f(u), which is taken to be a strickly positive function, represents the temperature-dependent resistivity. We also prove that solutions exist for all positive time and must enter a bounded region as t goes to infinity. © 1994.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalApplied Mathematics Letters
Volume7
Issue number3
Publication statusPublished - May 1994

Keywords

  • Nonlocal parabolic equations
  • Ohmic heating

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