### Abstract

In this note, we study questions of multiplicity and stability of stationary solutions of the nonlocal reaction-diffusion equation u_{t} = u_{xx}+?f{hook}(u) a + sh{phonetic} 0 1f{hook}(u)dx^{2} 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 language | English |
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Pages (from-to) | 1-6 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 7 |

Issue number | 3 |

Publication status | Published - May 1994 |

### Keywords

- Nonlocal parabolic equations
- Ohmic heating

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## Cite this

Frettas, P., & Grinfeld, M. (1994). Stationary solutions of an equation modelling ohmic heating.

*Applied Mathematics Letters*,*7*(3), 1-6.