Generic behaviour of one-dimensional blow up patterns
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 3, pp. 381-450. 
@article{ASNSP_1992_4_19_3_381_0,
     author = {Herrero, M. A. and Vel\'azquez, J. J. L.},
     title = {Generic behaviour of one-dimensional blow up patterns},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {381--450},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {3},
     year = {1992},
     mrnumber = {1205406},
     zbl = {0798.35081},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1992_4_19_3_381_0/}
}
TY  - JOUR
AU  - Herrero, M. A.
AU  - Velázquez, J. J. L.
TI  - Generic behaviour of one-dimensional blow up patterns
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1992
SP  - 381
EP  - 450
VL  - 19
IS  - 3
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1992_4_19_3_381_0/
LA  - en
ID  - ASNSP_1992_4_19_3_381_0
ER  - 
%0 Journal Article
%A Herrero, M. A.
%A Velázquez, J. J. L.
%T Generic behaviour of one-dimensional blow up patterns
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1992
%P 381-450
%V 19
%N 3
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1992_4_19_3_381_0/
%G en
%F ASNSP_1992_4_19_3_381_0
Herrero, M. A.; Velázquez, J. J. L. Generic behaviour of one-dimensional blow up patterns. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 3, pp. 381-450. http://www.numdam.org/item/ASNSP_1992_4_19_3_381_0/

[B1] A. Bressan, On the asymptotic shape of blow up, Indiana Univ. Math. J., 39, 4 (1990), 947-960. | MR | Zbl

[B2] A. Bressan, Stable blow up patterns, J. Differential Equations, 98 (1992), 57-75. | MR | Zbl

[BE] J. Bebernes - D. Eberly, Mathematical problems from combustion theory, Appl. Math. Sci. 83, Springer (1989). | MR | Zbl

[CM] X.Y. Chen - H. Matano, Convergence, asymptotic periodicity and finite point blow up in one-dimensional semilinear heat equations, J. Differential Equations, 78 (1989), 160-190. | MR | Zbl

[D] J.W. Dold, Analysis of the early stage of thermal runaway, Quart. J. Mech. Appl. Math. 38 (1985), 361-387. | Zbl

[F] A. Friedman, Partial Differential Equations of parabolic type, Robert E. Krieger Co (1983).

[FK] S. Filippas - R.V. Kohn, Refined asymptotics for the blow up of u t - Δu = up, Comm. Pure. Appl. Math., XLV (1992), 821-869. | Zbl

[FM] A. Friedman - J.B. Mcleod, Blow up of positive solutions of semilinear heat equations, Indiana Univ. Math. J., 34 (1985), 425-447. | MR | Zbl

[Fu] H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), 109-124. | Zbl

[GHV] V.A. Galaktionov - M.A. Herrero - J.J.L. Velázquez, The space structure near a blow up point for semilinear heat equations, Soviet J. Comput. Math. and Math. Physics, 31 (1991), 399-411. | MR | Zbl

[GK1] Y. Giga - R.V. Kohn, Asymptotically self-similar blow up of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), 297-319. | MR | Zbl

[GK2] Y. Giga - R.V. Kohn, Characterizing blow up using similarity variables, Indiana Univ. Math. J., 36 (1987), 1-40. | MR | Zbl

[GK3] Y. Giga - R.V. Kohn, Nondegeneracy of blow up for semilinear heat equations, Comm. Pure Appl. Math., 42 (1989), 845-884. | MR | Zbl

[GP] V.A. Galaktionov - S.A. Posashkov, Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations, Differential Equations, 22, 7 (1986), 116-1183. | MR | Zbl

[HV1] M.A. Herrero - J.J.L. Velázquez, Blow up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. H. Poincaré, to appear. | Numdam | MR | Zbl

[HV2] M.A. Herrero - J.J.L. Velázquez, Flat blow up in one-dimensional semilinear heat equations, Differential Integral Equations, Vol. 5, n° 5 (1992), 973-997. | MR | Zbl

[HV3] M.A. Herrero - J.J.L. Velázquez, Blow up profiles in one-dimensional, semilinear parabolic problems, Comm. Partial Differential Equations, 17, 182, (1992), 205-219. | MR | Zbl

[HV4] M.A. Herrero - J.J.L. Velázquez, Plane structures in thermal runaway, Israel J. Math., to appear. | MR | Zbl

[HSS] L.M. Hocking - K. Stewartson - J.T. Stuart, A nonlinear instability burst in plane parallel flow, J. Fluid Mech. J1 (1972), 705-735. | Zbl

[LM] J.L. Lions - B. Malgrange, Sur l'unicité retrograde, Math. Scand. 8 (1960), 277-286. | MR | Zbl

[M] F. Merle, Solution of a nonlinear heat equation with arbitrarily given blow up points, Comm. Pure. Appl. Math., to appear. | MR | Zbl

[MW] C.E. Müller - F.B. Weissler, Single point blow up for a general semilinear heat equation, Indiana Univ. Math. J., 34 (1983), 881-913. | MR | Zbl

[V] J.J.L. Velázquez, Local behaviour near blow up points for semilinear parabolic equations, J. Differential Equations, to appear. | MR | Zbl

[W] F.B. Weissler, Single point blow up of semilinear initial value problems, J. Differential Equations, 55 (1984), 204-224. | MR | Zbl