Stationary solutions of an equation modelling ohmic heating

Pedro Frettas; M. Grinfeld

Stationary solutions of an equation modelling ohmic heating

Pedro Frettas, M. Grinfeld

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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)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 language	English
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

Cite this

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AB - 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.

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KW - Ohmic heating

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Stationary solutions of an equation modelling ohmic heating

Abstract

Keywords

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