A non-local thermistor problem

Allegretto, W.; Xie, Hong

doi:10.1017/s0956792500001686

Cited by 17 publications

(10 citation statements)

References 19 publications

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“…Mathematical investigations have been undertaken by Cimatti and Prodi, [41] [123][124][125][126][127][128][129][130], and others. Here we consider at first primarily the steady-state problem and follow the presentation of Xie and Allegretto, [122], [10], Xie, [120] , and Allegretto and Barabanova, [4]. The next result is quite similar in approach to those considered in the earlier sections.…”

Section: (T ) K(t ) → 0 As T → ∞ May Arise In Applications the Secomentioning

confidence: 89%

Drift-Diffusion Equations and Applications

Allegretto

2003

Mathematical Problems in Semiconductor Physics

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We shall discuss a variety of drift-diffusion equations and their properties. The choice is not intended to be comprehensive, rather it reflects to considerable extent the author's interests, and the cited references mention numerous other related papers. We begin with a short description of results for the "classical" drift-diffusion equations for semiconductors, then consider variations and, finally, an application. To minimize technical difficulties we shall always assume that all known functions are smooth in their variables otherwise specified, and all mathematically irrelevant constants will be set to unity. The interested reader will find more general situations discussed in the given references.The solutions to be found are also to be understood in the usual weak sense. Nevertheless we shall almost always use classical notation to make the key steps evident. Again, a more precise formulation can be found in the references.

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Section: (T ) K(t ) → 0 As T → ∞ May Arise In Applications the Secomentioning

confidence: 89%

Drift-Diffusion Equations and Applications

Allegretto

2003

Mathematical Problems in Semiconductor Physics

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“…Such materials are being used in switches and electric surge protecting devices, among other applications. It was brought to the Oxford Study Groups with Industry in the mid 80's and has received, as a result, considerable attention in the mathematical literature, see, e.g., [1,2,3,5,7,8,9,12,15,16,19,24,25,26,28] and references therein. Related problems can be found in [21] and [27,14].…”

Section: Introductionmentioning

confidence: 99%

Existence for the thermoviscoelastic thermistor problem

Kuttler

Shillor

Fernández

2008

Differ Equ Dyn Syst

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The existence of a weak solution to a dynamic model for a thermistor, which takes into account the thermoelastic properties of the device, is established. The model consists of a coupled system of the equations of dynamic thermoviscoelasticity, the heat equation with the Joule heating term, and the quasistatic charge conservation equation. The system is strongly nonlinear since the electrical conductivity is assumed to be temperature dependent, and the Joule heating term is quadratic in the gradient of the electric potential. The existence of a solution is obtained by considering a sequence of approximate time-retarded problems. After obtaining the necessary a priori estimates, a solution of the problem is found by passing to the approximation limit. The uniqueness of the solution remains an open problem. c 2008 Foundation for Scientific Research and Technological Innovation(FSRTI). All rights reserved.MSC: 74D05, 74F05, 74H20, 74H30

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“…For another configuration of the conductor-thermistor, the so-called narrowing process, which considers that only a small part, and not the whole of the thermistor, is cylindrical, see [5]. Also, steady states of the full problem (1.1), (1.2) were investigated in [1,10,11]. Equation (1.3) can also be used to describe thermoviscous flow of linear materials.…”

Section: Introductionmentioning

confidence: 99%

On the Blow-Up of the Non-Local Thermistor Problem

Kavallaris

Nadzieja²

2007

Proceedings of the Edinburgh Mathematical Society

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The conditions under which the solution of the non-local thermistor problemblows up are investigated. We assume that f (s) is a decreasing function and that it is integrable in (0, ∞). Considering a suitable functional we prove that for all λ > 0 the solution of the Neumann problem blows up in finite time. The same result is obtained for the Robin problem under the assumption that λ is sufficiently large (λ 1). In the proof of existence of blow-up for the Dirichlet problem we use the subsolution technique. We are able to construct a blowing-up lower solution under the assumption that either λ > λ * or 0 < λ < λ * , for some critical value λ * , and that the initial condition is sufficiently large provided also that f (s) satisfies the decay condition

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A non-local thermistor problem

Cited by 17 publications

References 19 publications

Drift-Diffusion Equations and Applications

Drift-Diffusion Equations and Applications

Existence for the thermoviscoelastic thermistor problem

On the Blow-Up of the Non-Local Thermistor Problem

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