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All issues Volume 10 / No 6 (2015) Math. Model. Nat. Phenom., 10 6 (2015) 77-89 References
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Issue
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
Page(s) 77 - 89
DOI https://doi.org/10.1051/mmnp/201510607
Published online 02 October 2015
  1. H. Amann. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev., 18 (1976), 620–709. [CrossRef] [MathSciNet] [Google Scholar]
  2. S.N. Antontsev, M. Chipot. Analysis of blowup for the thermistor problem. Siberian. Math. Jl., 38 (1997), 827–841. [CrossRef] [Google Scholar]
  3. J. Bebernes, S. Bricher. Final time blowup profiles for semilinear parabolic equations via center manifold theory. SIAM Jl. Math. Anal., 23 (1992), No. 4, 852–869. [CrossRef] [Google Scholar]
  4. J. Bebernes, A.A. Lacey. Global existence and finite-time blow-up for a class of nonlocal parabolic problems. Adv. Diff. Eqns., 2 (1997), No. 6, 927–53. [Google Scholar]
  5. J. Bebernes, D. Eberly. Mathematical problems fromcombustion theory. Springer, New York, 1989. [Google Scholar]
  6. G. Cimatti. The stationary thermistor problem with a current limiting device. Proc. Roy. Soc. Edin., 116A (1990), 79–84. [CrossRef] [Google Scholar]
  7. M. Cologna, B. Rashkova, R. Raj. Flash sintering of nanograin zirconia in < 5s at 850°C. J. Am. Ceram. Soc., 93 (2010), No. 11, 3556–3559. [CrossRef] [Google Scholar]
  8. A.C. Fowler, I. Frigaard, S.D. Howison. Temperature surges in current-limiting circuit devices. SIAM Jl. Appl. Math., 52 (1992), 998–1011. [CrossRef] [Google Scholar]
  9. J.S.C. Francis, M. Cologna, R. Raj. Particle size effects in flash sintering. J. Eur. Ceram. Soc., 32 (2012), 3129–3136. [CrossRef] [Google Scholar]
  10. J.S.C. Francis, R. Raj. Influence of the field and the current limit on flash sintering at isothermal furnace temperatures. J. Eur. Ceram. Soc., 96 (2013), No. 9, 2754–2758. [CrossRef] [Google Scholar]
  11. P. Freitas. A nonlocal Sturm-Liouville eigenvalue problem. Proc. Roy. Soc. Ed., 124A (1994), No. 1, 169–188. [CrossRef] [Google Scholar]
  12. A. Friedman, B. McLeod. Blowup of positive solutions of semilinear heat equations. Indiana Univ. Jl. Maths., 34 (1985), 425–477. [CrossRef] [Google Scholar]
  13. I.M. Gelfand. Some problems in the theory of quasilinear equations. Amer. Math. Soc. Trans., 29 (1963), 295–381. [Google Scholar]
  14. S. Grasso, Y. Sakka, N. Redntorff, C. Hu, G. Maizza, H. Borodianska, O. Vasylkiv. Modeling of the temperature distribution of flash sintered zirconia. J. Ceram. Soc. Japan, 119 (2011), No. 2, 144–146. [CrossRef] [Google Scholar]
  15. S. Grasso, T. Saunders, H. Porwal, O. Cedillos-Barraza, D.D. Jayaseelan, W.E. Lee, M.J. Reece. Flash Spark Plasma Sintering (FSPS) of Pure ZrB2. J. Am. Ceram. Soc., 97 (2014), No. 8, 2405–2408. [CrossRef] [Google Scholar]
  16. M.A. Herrero, J.J.L. Velázquez. Blow-up profiles in one-dimensional. semilinear parabolic problems. Coms. PDEs., 17 (1992), No. 3, 205–219. [CrossRef] [Google Scholar]
  17. M.A. Herrero, J.J.L. Velázquez. Plane structures in thermal runaway. Israel Jl. Maths., 81 (1993), No. 3, 321–341. [CrossRef] [Google Scholar]
  18. D.D. Joseph, T.S. Lundgren. Quasilinear Dirichlet problems driven by positive sources. Arch. Rat. Mech. Anal., 49 (1973), 241–269. [Google Scholar]
  19. H.B. Keller, D.S. Cohen. Some positone problems suggested by nonlinear heat generation. Jl. Math. Mech., 16 (1967), 1361–1376. [Google Scholar]
  20. A.A. Lacey. Mathematical analysis of thermal runaway for spatially inhomogeneous reactions. SIAM Jl. Appl. Maths., 43 (1983), 1350–1366. [CrossRef] [Google Scholar]
  21. A.A. Lacey. Thermal runaway in a non-local problem modelling ohmic heating. I: Model derivation and some special cases. Eu. Jl. Appl. Maths., 6 (1995), 127–144. [Google Scholar]
  22. A.A. Lacey. Thermal runaway in a non-local problem modelling ohmic heating. II: General proof of blow-up and asymptotics of runaway. Eu. Jl. Appl. Maths., 6 (1995), 201–224. [Google Scholar]
  23. K.S. Naik, V.M. Sglavo, R. Raj. Flash sintering as a nucleation phenomenon and a model thereof. J. Eur. Ceram. Soc., 34 (2014), 4063–4067. [CrossRef] [Google Scholar]
  24. R. Raj. Joule heating during flash-sintering. J. Eur. Ceram. Soc., 32 (2012), 2293–2301. [CrossRef] [Google Scholar]
  25. D. Sattinger. Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. Jl., 21 (1972), 979–1000. [Google Scholar]
  26. R.I. Todd, E. Zapata-Solvas, R.S. Bonilla, T. Sneddon, P.R. Wilshaw. Electrical characteristics of flash sintering: thermal runaway of Joule heating. To appear in J. Eur. Ceram. Soc. (2015). [Google Scholar]
  27. E. Zapata-Solvas, S. Bonilla, P.R. Wilshaw, R.I. Todd. Preliminary investigation of flash sintering of SiC. J. Eur. Ceram. Soc., 33 (2013), 2811–2816. [CrossRef] [Google Scholar]

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