Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion

R. Monneau; G. S. Weiss

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 4, page 1207-1222
  • ISSN: 0294-1449

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Monneau, R., and Weiss, G. S.. "Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion." Annales de l'I.H.P. Analyse non linéaire 26.4 (2009): 1207-1222. <http://eudml.org/doc/78886>.

@article{Monneau2009,
author = {Monneau, R., Weiss, G. S.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {high activation energy; Stefan problem; free boundary; self-propagating high temperature synthesis; PDE-ODE system; memory term; Matkowsky-Sivashinsky scaling},
language = {eng},
number = {4},
pages = {1207-1222},
publisher = {Elsevier},
title = {Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion},
url = {http://eudml.org/doc/78886},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Monneau, R.
AU - Weiss, G. S.
TI - Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 4
SP - 1207
EP - 1222
LA - eng
KW - high activation energy; Stefan problem; free boundary; self-propagating high temperature synthesis; PDE-ODE system; memory term; Matkowsky-Sivashinsky scaling
UR - http://eudml.org/doc/78886
ER -

References

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  1. [1] Bayliss A., Matkowsky B.J., Aldushin A.P., Dynamics of hot spots in solid fuel combustion, Physica D166 (1–2) (2002) 104-130. Zbl1036.80503MR1913748
  2. [2] Berestycki H., Hamel F., Front propagation in periodic excitable media, Comm. Pure Appl. Math.55 (8) (2002) 949-1032. Zbl1024.37054MR1900178
  3. [3] Berestycki H., Nicolaenko B., Scheurer B., Traveling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal.16 (6) (1985) 1207-1242. Zbl0596.76096MR807905
  4. [4] A. Bonnet, E. Logak, Instability of travelling waves in solid combustion for high activation energy, Preprint. 
  5. [5] Duchon J., Robert R., Évolution d'une interface par capillarité et diffusion de volume. I. Existence locale en temps, Ann. Inst. H. Poincaré Anal. Non Linéaire1 (5) (1984) 361-378. Zbl0572.35051MR779874
  6. [6] Ladyženskaja O.A., Solonnikov V.A., Ural'ceva N.N., Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, vol. 23, American Mathematical Society, Providence, RI, 1967, Translated from the Russian by S. Smith. Zbl0174.15403MR241822
  7. [7] Logak E., Loubeau V., Travelling wave solutions to a condensed phase combustion model, Asymptotic Anal.12 (4) (1996) 259-294. Zbl0865.34016MR1402978
  8. [8] Matkowsky B.J., Sivashinsky G.I., Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math.35 (3) (1978) 465-478. Zbl0404.76074MR507948
  9. [9] Monneau R., Weiss G.S., Self-propagating high temperature synthesis in the high activation energy regime, Acta Math. Univ. Comenian.76 (1) (2007) 99-109. Zbl1136.80007MR2331057
  10. [10] Rodrigues J.-F., Obstacle Problems in Mathematical Physics, North-Holland Mathematics Studies, vol. 134, North-Holland Publishing Co., Amsterdam, 1987. Zbl0606.73017MR880369
  11. [11] Zeldovich J.B., Frank-Kamenetskii D.A., A theory of thermal propagation of flame, Acta Physico-chimica URSS9 (1938). 

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