Global existence for reaction-diffusion systems modelling ignition

Archive for Rational Mechanics and Analysis

Volumn 142, Issue 3, 1998, Pages 219-251

  Herrero, Miguel A ^a   Lacey, Andrew A ^a   Velázquez, Juan J L ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032361797     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050091     Document Type: Article

References (25)

1. D. ANDREUCCI, M. A. HERRERO & J. J. L. VELAZQUEZ: Liouville theorems and blow-up behaviour in semilinear reaction-diffusion systems. Ann. Inst. Henri Poincaré 14 (1997), 1-53.
2. C. ALVAREZ-PEREIRA & J. M. VEGA: Global stability of a premixed reaction zone (time-dependent Liñan's problem), SIAM J. Math. Anal. 21 (1990), 884-904.
3. D. G. ARONSON: Non-negative solutions of linear parabolic equations. Annali Sc. Norm. Sup. Pisa 22 (1968), 607-694.
4. A. BARABAROVA: On the global existence of solutions of a reaction-diffusion equation with exponential nonlinearity. Proc. Amer. Math. Soc. 122 (1994), 827-831.
5. max for the solution of a semilinear heat equation. J. Func. Anal. 71 (1987), 142-174.
6. J. BEBERNES & D. EBERLY: Mathematical problems from combustion theory, Springer (1989).
7. J. BEBERNES & A. A. LACEY: Finite-time blow-up for a particular parabolic system. SIAM J. Math. Anal. 21 (1990), 1415-1425.
8. J. BEBERNES & A. A. LACEY: Finite-time blow-up for semilinear reactive-diffusive systems. J. Diff. Eqs. 96 (1992), 105-129.
9. J. DUOANDIKOETXEA: Análisis de Fourier. Ediciones de la Universidad Autónoma de Madrid (1991).
10. M. ESCOBEDO & M. A. HERRERO: Boundedness and blow-up for a semilinear reaction-diffusion system. J. Diff. Eq. 89 (1991), 176-202.
11. p. Comm. Pure Appl. Math. 45 (1992), 821-869.
12. S. FILIPPAS & F. MERLE: Modulation theory for the blow-up of vector valued nonlinear heat equations. J. Diff. Eq. 116 (1995), 119-148.
13. Y. GIGA & R. V. KOHN: Asymptotically self-similar blow-up of semilinear parabolic equations. Comm. Pure Appl. Math. 38 (1985), 297-319.
14. N. Springer Lecture Notes in Mathematics no 481 (1975).
15. S. L. HOLLIS, R. H. MARTIN & M. PIERRE: Global existence and boundedness in reaction-diffusion systems. SIAM J. Math. Anal. 18 (1987), 744-761.
16. M. A. HERRERO & J. J. L. VELAZQUEZ: Blow up behaviour of one-dimensional semilinear heat equations. Ann. Inst. Henri Poincaré 10 (1993), 131-189.
17. M. A. HERRERO & J. J. L. VELAZQUEZ: Blow-up profiles in one-dimensional, semilinear parabolic problems. Comm. in PDE 17 (1992), 205-219.
18. A. HARAUX & A. YOUKANA: On a result of K. Masuda concerning reaction-diffusion equations. Tohoku Math. J. 40 (1988), 159-163.
19. A. A. LACEY: Mathematical analysis of thermal runaway for spatially inhomogeneous reactions. SIAM J. Appl. Math. 43 (1983), 1350-1366.
20. A. A. LACEY & D. TZANETIS: Global existence and convergence to a singular steady state for a semilinear heat equation. Proc. Royal Soc. Edinburgh A105 (1987), 289-305.
21. A. A. LACEY & D. TZANETIS: Global, unbounded solutions to a parabolic equations. J. Diff. Eq. 101 (1993), 80-102.
22. K. MASUDA: On the global existence and asymptotic behaviour of reaction-diffusion equations. Hokkaido Math. J. 12 (1983), 360-370.
23. R. H. MARTIN & M. PIERRE: Nonlinear reaction-diffusion systems. In the book Nonlinear Equations in the Applied Sciences, W. F. AMES & C. ROGERS, eds. Academic Press (1991).
24. J. J. L. VELAZQUEZ: Classification of singularities for blowing up solutions in higher dimensions. Trans. Amer. Math. Soc. 338 (1993), 441-464.
25. J. J. L. VELAZQUEZ: Estimates on the (n - 1)-dimensional Hausdorff measure of the blow-up set for a semilinear heat equation. Indiana Univ. Math. J. 42 (1993), 445-476.