The global dynamics of isothermal chemical systems with critical nonlinearity

Nonlinearity

Volumn 16, Issue 3, 2003, Pages 1057-1074

  Li, Y ^a   Qi, Y W ^b  

^a UNIVERSITY OF IOWA   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242371751     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/3/315     Document Type: Article

References (18)

1. p bounds of solutions of the reaction-diffusion systems Commun. Partial Diff. Eqns 4 827-68
2. Avrin J D 1990 Qualitative theory for a model of laminar flames with arbitrary non-negative initial data J. Diff. Eqns 84 290-308
3. Berlyand L and Xin J 1995 Large time asymptotics of solutions to a model combustion system with critical nonlinearity Nonlinearity 8 161-78
4. Billingham J and Needham D J 1991 The development of traveling waves in quadratic and cubic autocatalysis with unequal diffusion rates: I. Permanent form travelling waves Phil. Trans. R. Soc. A 334 1-24
5. Billingham J and Needham D J 1991 The development of traveling waves in quadratic and cubic autocatalysis with unequal diffusion rates: II. An initial-value problem with an immobilized or nearly immobilized autocatalyst Phil. Trans. R. Soc. A 336 497-539
6. Bricmont J, Kupiainen A and Lin G 1994 Renormalization group and asymptotics of solutions of nonlinear parabolic equations Commun. Pure Appl. Math 47 893-922
7. Bricmont J, Kupiainen A and Xin J 1996 Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity J. Diff. Eqns 130 9-35
8. Feireisl E, Hilhorst D, Mimura M and Weidenfeld R On some reaction-diffusion systems with nonlinear diffusion arising in biology Preprint
9. Goldenfeld N, Martin O, Oono Y and Liu F 1990 Anomalous dimensions and the renormalization group in a nonlinear diffusion process Phys. Rev. Lett. 64 1361-4
10. Hollis S, Martin R and Pierre M 1987 Global existence and boundedness in reaction-diffusion systems SIAM J. Math. Anal. 18 744-61
11. m, with application to weak solutions Math. Z. 187 471-80
12. Martin R and Pierre M 1992 Nonlinear reaction-diffusion systems Nonlinear Equations in the Applied Sciences ed W F Ames and C Rogers (Boston, MA: Academic)
13. Masuda K 1983 On the global existence and asymptotic behavior of solutions of reaction-diffusion equations Hokkaido Math J. 12 360-70
14. Matkowsky B J and Sivashinsky G I 1979 An asymptotic derivation of two models in flame theory associated with the constant density approximation SIAM J. Appl. Math. 37 686-99
15. Metcalf M J, Merkin J H and Scott S K 1994 Oscillating wave fronts in isothermal chemical systems with arbitrary powers of autocatalysis Proc. R. Soc. A 447 155-74
16. Nishiura Y Mathematics of Patterns at press
17. 2 decay for weak solutions of the Navier-Stokes equation Arch. Rational Mech. Anal. 88 209-22
18. Sivashinsky G I 1983 Instability, pattern formation and turbulence in flames Ann. Rev. Fluid Mech. 15 179-99