Blow-up behavior in nonlocal vs local heat equations

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1. [BBL] J. Bebernes, A. Bressan and A. Lacey, Total blow-up versus single-point blow-up, J. Differ. Equations 73 (1988), 30-44. Zbl0674.35051
2. [BK] J. Bricmont and A. Kupiainen, Universality in blow-up for nonlinear heat equations, Nonlinearity 7 (1994), 539-575. Zbl0857.35018
3. [CM] X. Y. Chen and H. A. Matano, Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations, J. Differ. Equations 78 (1989), 160-190. Zbl0692.35013
4. [D] K. Deng, Nonlocal nonlinearity versus global blow-up, Math. Applicata (1995), 124-129. 
5. [FM] A. Friedman and J. B. McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447. Zbl0576.35068
6. [GK1] Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 8 (1985), 297-319. Zbl0585.35051
7. [GK2] Y. Giga and R. V. Kohn, Characterizing blowup using similarity variables, Indiana Univ. Math. J. 36 (1987), 1-40. Zbl0601.35052
8. [GK3] Y. Giga and R. V. Kohn, Nondegeneracy of blowup for semilinear heat equation, Comm. Pure Appl. Math. 42 (1989), 845-884. Zbl0703.35020
9. [HV] M. A. Herrero and J. J. L. Velázquez, Generic behaviour of one-dimensional blow up patterns, Annali Sc. Norm. Sup. Pisa 19, 3 (1992), 381-450. Zbl0798.35081
10. [MZ1] F. Merle and H. Zaag, Stability of blow-up profile for equation of the type $u_t=\Delta u+{\left|u\right|}^p-1u$, Duke Math. J. 86 (1997), 143-195. Zbl0872.35049
11. [MZ2] F. Merle and H. Zaag, Optimal estimates for blow-up rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math. 51 (1998), 139-196. 
12. [MW] C. E. Mueller and F. B. Weissler, Single point blow-up for general semilinear heat equation, Indiana Univ. Math. J. 34 (1985), 881-913. Zbl0597.35057
13. [S1] Ph. Souplet, Blow-up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal. 29 (1998), 1301-1334. Zbl0909.35073
14. [S2] Ph. Souplet, Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source, J. Differ. Equations 153 (1999), 374-406. Zbl0923.35077
15. [S3] Ph. Souplet, Some blow-up results for nonlocal reaction-diffusion equations, in: Actes du 3ème Congrès Européen sur les problèmes elliptiques et paraboliques (Pont-à-Mousson, juin 1997), Pitman Research Notes in Mathematics Series, n° 384, Addison Wesley Longman, 1998. 
16. [V1] J. J. L. Velázquez, Classification of singularities for blowing-up solutions in higher dimensions, Trans. Amer. Math. Soc. 338 (1993), 441-464. Zbl0803.35015
17. [V2] J. J. L. Velázquez, 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. Zbl0802.35073
18. [V3] J. J. L. Velázquez, Blow up for semilinear parabolic equations, in: Recent advances in partial differential equations, M. A. Herrero et al. (eds.), Res. Notes Appl. Math. 30, Masson, Paris, 1993, 131-145. 
19. [WW] M. Wang and Y. Wang, Properties of positive solutions for non-local reaction-diffusion problems, Math. Methods Appl. Sci. 19 (1996), 1141-1156. Zbl0990.35066
20. [W1] F. B. Weissler, Single point blow-up for a semilinear initial value problem, J. Differ. Equations 55 (1984), 204-224. Zbl0555.35061
21. [W2] F. B. Weissler, An $L^{\infty }$ blow-up estimate for a nonlinear heat equation, Comm. Pure Appl. Math. 38 (1985), 291-295. Zbl0592.35071