Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
|
|
---|---|---|
Page(s) | 90 - 112 | |
DOI | https://doi.org/10.1051/mmnp/201510608 | |
Published online | 02 October 2015 |
- M. R. Sidi Ammi, O. Mul. Error estimates for the Chernoff scheme to approximate a nonlocal problem, Proc. Estonian Acad. Sci. Phys. Maths., 56 (2007), 359–372. [Google Scholar]
- S. N. Antontsev, M. Chipot. The analysis of blow-up for the thermistor problem, Siberian Math. J., 38 (1997), 827–841. [Google Scholar]
- J. Bebernes, P. Talaga. Nonlocal problems modelling shear banding, Comm. Appl. Nonlinear Analysis, 3, (1996), 79–103. [Google Scholar]
- A. E. Berger, H. Brezis, J. C. W. Rogers. A numerical method for solving the problem ut − Δf(u) = 0, RAIRO Anal. Numer., 13, (1979), 297–312. [MathSciNet] [Google Scholar]
- M. Brokate, J. Sprekels. Hysteresis and Phase Transitions Appl.Math. Sci. Springer: New York, 1996. [Google Scholar]
- I.J. Hewitt, A.A. Lacey, R.I. Todd. A Mathematical Model for flash sintering, to appear in Math. Model. Nat. Phenom. [Google Scholar]
- D. Hömberg, E. Rocca. A model for resistance welding including phase transitions and Joule heating, Math. Meth. Appl. Sciences, 34 (2011), 2077–2088. [CrossRef] [Google Scholar]
- N. I. Kavallaris. Asymptotic behaviour and blow-up for a nonlinear diffusion problem with a non-local source term, Proc. Edinb. Math. Soc., 47 (2004), 375–395. [CrossRef] [MathSciNet] [Google Scholar]
- N. I. Kavallaris, A.A. Lacey, C.V. Nikolopoulos, C. Voong. Behaviour of a non-local equation modelling linear friction welding, IMA J. Appl. Mathematics, 72 (2007), 597–616. [CrossRef] [Google Scholar]
- N. I. Kavallaris, T. Nadzieja. On the blow-up of the non-local thermistor problem, Proc. Edinb. Math. Soc., 50 (2007), 389–409. [CrossRef] [MathSciNet] [Google Scholar]
- N.I. Kavallaris, T. Suzuki. On the finite-time blow-up of a non-local parabolic equation describing chemotaxis, Differential Integral Equations, 20, (2007), 293–308. [MathSciNet] [Google Scholar]
- A. A. Lacey. Thermal runaway in a nonlocal problem modelling ohmic heating, Part I, Model derivation and some special cases, European. J. Appl. Math., 6 (1995), 127–144. [CrossRef] [MathSciNet] [Google Scholar]
- E.A. Latos, D. E. Tzanetis. Existence and blow-up of solutions for a non-local filtration and porous medium problem, Proc. Edinb. Math. Soc., 53 (2010), 195–209. [CrossRef] [MathSciNet] [Google Scholar]
- E.A. Latos, D. E. Tzanetis. Grow-up of critical solutions for a non-local porous medium problem with Ohmic heating source, Nonlinear Differ. Equ. Appl., 17 (2010), 137–151. [CrossRef] [Google Scholar]
- R. H. Nochetto, C. Verdi. Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., 25, (1988), 784–814. [CrossRef] [MathSciNet] [Google Scholar]
- R. H. Nochetto, C. Verdi. An efficient linear scheme to approximate parabolic free boundary problems: Error estimates and implementation, Mathematics of Computation, 51 (1988), 27–53. [CrossRef] [Google Scholar]
- N. Saunders, X. Li, A. P. Miodownik, J-Ph. Schillé. Modelling of the thermo-physical and physical properties relevant to solidification, In Advanced Solidification Processes X, Stefanescu D, Warren JA, Jolly MR, Krane MJM (eds). TMS: Warrendale, PA, (2003); 669. [Google Scholar]
- I. Steinbach, M. Apel. Multi phase field model for solid state transformation with elastic strain, Physica D, 217 (2006), 153–160. [CrossRef] [Google Scholar]
- D. E. Tzanetis. Blow-up of radially symmetric solutions of a non-local problem modelling ohmic heating, Electron. J. Diff. Eqns, 11 (2002), 1–26. [Google Scholar]
- D. E. Tzanetis, P. M. Vlamos. A nonlocal problem modelling ohmic heating with variable thermal conductivity, Nonlin. Analysis, 2 (2001), 443–454. [CrossRef] [Google Scholar]
- D. E. Tzanetis, P. M. Vlamos. Some interesting special cases of a non-local problem modelling Ohmic heating with variaable thermal conductivity, Proc. Edinb. Math. Soc., 44 (2001), 58559–5. [CrossRef] [Google Scholar]
- J.L. Vazquez. The Porous Medium Equation: Mathematical Theory, Oxford Science Publications, 2007. [Google Scholar]
- C. Verdi. On the numerical approach to a two-phase Stefan problem with non-linear flux, Calcolo, 22 (1985), 351–381. [CrossRef] [MathSciNet] [Google Scholar]
- G. Wolansky. A critical parabolic estimate and application to non-local equations arising in chemotaxis, Appl. Anal., 66 (1997), 291–321. [CrossRef] [Google Scholar]
- Ya. B. Zel’dovich, Yu.P. Raizer. Physics of Shock Wavesand High-Temperature Hydrodynamic Phenomena, Vol. II, Academic Press, New York. [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.