Stability and multiplicity of solutions for the thermistor problem

Annali di Matematica Pura ed Applicata

Volumn 181, Issue 2, 2002, Pages 181-212

  Cimatti, Giovanni ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Asymptotic stability; Hale LaSalle invariance principle; Liapunov functional; Thermistor

Indexed keywords

EID: 14744306903     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s102310100034     Document Type: Article

References (19)

1. Allegretto, W., Xie, H.: Existence of solutions for the time-dependent thermistor problem. IMA J. Appl. Math. 48, 271-281 (1992)
2. Amann, H.: Periodic solutions of semilinear parabolic equations. In: A Collection of Papers to honor Professor E.H. Rothe. Academic Press 1971
3. Antonsev, S.N., Chipot, M.: The thermistor problem, smoothness, uniqueness, blowup. SIAM J. Math. Anal. 25, 1128-1156 (1994)
4. Cesari, L.: Optimization Theory and Applications. Springer 1983
5. Chipot, M., Cimatti, G.: A uniqueness result for the thermistor problem. Eur. J. Appl. Math. 2, 97-103 (1991)
6. Cimatti, G.: Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions. Quart. Appl. Math. 47, 117-121 (1989)
7. Cimatti, G.: The stationary thermistor problem with a current limiting device. Proc. Roy. Soc. Edin. 116A, 79-84 (1990)
8. Cimatti, G.: On the stability of the solution of the thermistor problem. Appl. Anal. 73, 407-423 (1999)
9. Cimatti, G., Prodi, G.: Existence results for a non-linear elliptic system modelling a temperature dependent electrical resistor, Ann. Mat. Pura Appl. 152, 227-236 (1988)
10. Hale, J.K.: Dynamical systems and stability. J. Math. Anal. 26, 39-59 (1969)
11. Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lectures Notes in Mathematics, 840, Springer 1981
12. Hyde, F.J.: Thermistors. London: Iliffe Books 1971
13. Yin, H.-M., Chen, X.: On a strongly coupled elliptic-parabolic system. University of Notre Dame, USA, November 1994. Preprint
14. Howison, S.D., Rodrigues, J.F., Shillor, M.: Stationary solutions to the thermistor problem. JMAA 174, 573-588 (1993)
15. Lacey, A.A.: Thermal runaway in a non-local problem modelling ohmic heating: Part I: model derivation and some special cases. Eur. J. Appl. Math. 6, 127-144 (1995)
16. Lacey, A.A.: Thermal runaway in a non-local problem modelling ohmic heating: Part II: general proof of blow-up and asymptotic of runaway. Eur. J. Appl. Math. 6, 201-224 (1995)
17. Ladyzenskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, A.M.S. 1968
18. Reid, T.W.: A matrix differential equation of Riccati type. Amer. J. Math. 68, 237-246 (1946)
19. Components and Materials, non-linear resistors, March 1984, Applications Notes