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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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. {\textcopyright} 1994.",

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AU - Frettas, Pedro

AU - Grinfeld, M.

PY - 1994/5

Y1 - 1994/5

N2 - 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.

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.

KW - Nonlocal parabolic equations

KW - Ohmic heating

UR - https://www.scopus.com/pages/publications/38149146253

M3 - Article

SN - 0893-9659

VL - 7

SP - 1

EP - 6

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 3

ER -

Stationary solutions of an equation modelling ohmic heating

Abstract

Keywords

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