|
|
|
|
References
|
|
| |
| 1. |
K. N. Chueh, C. C. Conley, J. A. Smoller, “Positively invariant regions for systems of
nonlinear diffusion equations”, Indiana Univ. Math. J., 26:2 (1977), 373–392    |
| 2. |
V. V. Churbanov, “Primer sistemy reaktsii s diffuziei, v kotoroi diffuzionnye
chleny privodyat k vzryvu”, Dokl. AN SSSR, 310:6 (1990), 1308–1309  |
| 3. |
E. Conway, D. Hoff, J. Smoller, “Large time behavior of solutions of nonlinear
reaction-diffusion equations”, SIAM J. Appl. Math., 35:1 (1978), 1–16 |
| 4. |
M. Fila, H. Matano, “Blow-up in nonlinear heat equations from the dynamical
systems point of view”, Handbook of Dynamical Systems, 2, North-Holland, Amsterdam, 2002, 723–758 |
| 5. |
M. Fila, H. Ninomiya, J. L. Vázquez, “Dirichlet boundary conditions can prevent blow-up in
reaction-diffusion equations and systems”, Discrete Contin. Dynam. Systems A, 14:1 (2006), 63–74 |
| 6. |
Y. Giga, R. V. Kohn, “Characterizing blowup using similarity variables”, Indiana Univ. Math. J., 36:1 (1987), 1–40 |
| 7. |
M. Guedda, M. Kirane, “Diffusion terms in systems of reaction diffusion equations
can lead to blow up”, J. Math. Anal. Appl., 218:1 (1998), 325–327 |
| 8. |
J. K. Hale, “Large diffusivity and asymptotic behavior in parabolic systems”, J. Math. Anal. Appl., 118:2 (1986), 455–466 |
| 9. |
H. A. Levine, “The role of critical exponents in blowup theorems”, SIAM Rev., 32:2 (1990), 262–288 |
| 10. |
C. P. Lo, A blowup problem of reaction diffusion equation
related to the diffusion induced blowup phenomenon, arXiv: math/0307397 |
| 11. |
N. Mizoguchi, H. Ninomiya, E. Yanagida, “Diffusion-induced blowup in a nonlinear parabolic system”, J. Dynam. Differential Equations, 10:4 (1998), 619–638 |
| 12. |
J. Morgan, “On a question of blow-up for semilinear parabolic systems”, Differential Integral Equations, 3:5 (1990), 973–978 |
| 13. |
H. Ninomiya, H. F. Weinberger, “Pest control may make the pest population explode”, Z. Angew. Math. Phys., 54:5 (2003), 869–873 |
| 14. |
H. Ninomiya, H. F. Weinberger, “On $p$-homogeneous systems of differential equations and their linear perturbation”, Appl. Anal., 85:1–3 (2006), 225–247 |
| 15. |
M. Pierre, D. Schmitt, “Blowup in reaction-diffusion systems with dissipation of mass”, SIAM. J. Math. Anal., 28:2 (1997), 259–269 |
| 16. |
M. Pierre, D. Schmitt, “Blowup in reaction-diffusion systems with dissipation of mass”, SIAM Rev., 42:1 (2000), 93–106 |
| 17. |
N. Rashevsky, “An approach to the mathematical biophysics of biological
self-regulation and of cell polarity”, Bull. Math. Biophys., 2 (1940), 15–25 |
| 18. |
A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, A. P. Mikhailov, Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh
uravnenii, Nauka, M., 1987 |
| 19. |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Grundlehren Math. Wiss., 258, Springer-Verlag, New York, 1983  |
| 20. |
Ph. Souplet, “A note on diffusion-induced blow-up”, J. Differential Equations (to appear) |
| 21. |
A. M. Turing, “The chemical basis of morphogenesis”, Philos. Trans. Roy. Soc. London, B237:641 (1952), 37–72 |
| 22. |
L. Wang, M. Y. Li, “Diffusion-driven instability in reaction-diffusion systems”, J. Math. Anal. Appl., 254:1 (2001), 138–153 |
| 23. |
M. Wang, Q. Zhang, “A note on a question of blow-up for semilinear parabolic equations”, J. Math. Anal. Appl., 198:1 (1996), 289–300 |
| 24. |
H. F. Weinberger, “Invariant sets for weakly coupled parabolic and elliptic systems”, Rend. Mat. (6), 8 (1975), 295–310 |
| 25. |
H. F. Weinberger, “An example of blowup produced by equal diffusions”, J. Differential Equations, 154:1 (1999), 225–237 |
| 26. |
E. Yanagida, “Mini-maximizers for reaction-diffusion systems
with skew-gradient structure”, J. Differential Equations, 179:1 (2002), 311–335 |
| 27. |
T. Yoshizawa, Stability Theory by Liapunov's Second Method, Math. Soc. Japan, Tokyo, 1966 |
