The thermistor problem with Robin boundary condition

被引：2

作者：

Cimatti, Giovanni ^{[1
]}

机构：

[1] Dept Math, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

来源：

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA | 2016年 / 135卷

关键词：

Thermistor problem; Robin boundary condition; existence; uniqueness of solutions; EXISTENCE;

D O I：

10.4171/RSMUP/135-10

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the thermistor problem with Robin boundary condition for the temperature. A theorem of existence is proved using the compensated compactness method. For the one-dimensional case a result of non-existence and non-uniqueness is also given.

引用

页码：175 / 193

页数：19

共 12 条

[1] EXISTENCE RESULTS FOR A NONLINEAR ELLIPTIC SYSTEM MODELING A TEMPERATURE-DEPENDENT ELECTRICAL RESISTOR [J].

CIMATTI, G ;

PRODI, G .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1988, 152 :227-236

[2] Remarks on the existence, uniqueness and semi-explicit solvability of systems of autonomous partial differential equations in divergence form with constant boundary conditions [J].

Cimatti, Giovanni .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2011, 141 :481-495

[3] TEMPERATURE SURGES IN CURRENT-LIMITING CIRCUIT DEVICES [J].

FOWLER, AC ;

FRIGAARD, I ;

HOWISON, SD .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (04) :998-1011

[4]

HOWISON S. D., 2005, CAMBRIDGE TEXTS APPL

[5] STATIONARY SOLUTIONS TO THE THERMISTOR PROBLEM [J].

HOWISON, SD ;

RODRIGUES, JF ;

SHILLOR, M .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 174 (02) :573-588

[6]

Hyde F.J., 1971, THERMISTORS

[7]

KINDERLEHERER D., 1980, PURE APPL MATH, V88

[8]

Lacey A A., 1995, Eur. J. Appl. Math, V6, P201, DOI [10.1017/S0956792500001807, DOI 10.1017/S0956792500001807]

[9]

NECAS J., 1967, METHODES DIRECTES TH

[10]

PROTTER M. H., 1967, MAXIMUM PRINCIPLE DI

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