Free Access
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
Page(s) 77 - 89
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.