no. 3
On the blowup of multidimensional semilinear heat equations
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 3, pp. 313-344 
@article{AIHPC_1993__10_3_313_0,
     author = {Filippas, Stathis and Liu, Wenxiong},
     title = {On the blowup of multidimensional semilinear heat equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {313--344},
     year = {1993},
     publisher = {Gauthier-Villars},
     volume = {10},
     number = {3},
     mrnumber = {1230711},
     zbl = {0815.35039},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1993__10_3_313_0/}
}
TY  - JOUR
AU  - Filippas, Stathis
AU  - Liu, Wenxiong
TI  - On the blowup of multidimensional semilinear heat equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1993
SP  - 313
EP  - 344
VL  - 10
IS  - 3
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPC_1993__10_3_313_0/
LA  - en
ID  - AIHPC_1993__10_3_313_0
ER  - 
%0 Journal Article
%A Filippas, Stathis
%A Liu, Wenxiong
%T On the blowup of multidimensional semilinear heat equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 1993
%P 313-344
%V 10
%N 3
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPC_1993__10_3_313_0/
%G en
%F AIHPC_1993__10_3_313_0
Filippas, Stathis; Liu, Wenxiong. On the blowup of multidimensional semilinear heat equations. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 3, pp. 313-344. https://www.numdam.org/item/AIHPC_1993__10_3_313_0/

[1] J. Bebernes and S. Bricher, Final Time Blowup Profiles For Semilinear Parabolic Equations Via Center Manifold Theory, preprint. | MR

[2] J. Bebernes and D. Eberly, A description of self similar blow up for dimensions n ≧ 3, Ann. Inst. H. Poincaré, Anal. Non lineaire, Vol. 5, 1988, pp. 1-22. | Zbl | MR | Numdam

[3] M. Berger and R.V. Kohn, A rescalling algorithm for the numerical calculation of blowing up solutions, Comm. Pure Appl., Math., Vol. 41, 1988, pp. 841-863. | Zbl | MR

[4] A. Bressan, Stable Blow-up Patterns, J. Diff. Eqns., Vol. 98, 1992, pp. 947-960. | Zbl | MR

[5] X.-Y. Chen and H. Matano, Convergence, asymptotic periodicity, and finite-point blowup in one-dimensional semilinear heat equations, J. Diff. Eqns., Vol. 78, 1989, pp. 160-190. | Zbl | MR

[6] J. Carr, Applications of centre manifold theory, Springer-Verlag, New York, 1981. | Zbl | MR

[7] S. Filippas and R.V. Kohn, Refined Asymptotic for the blowup of ut - Δu = up, Comm. Pure Appl. Math., Vol. 45, 1992, pp. 821-869. | Zbl | MR

[8] A. Friedman, Blow-up of Solutions of Nonlinear Heat and Wave Equations, prcprint.

[9] A. Friedman and Mcleod B., Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J., Vol. 34, 1985, pp. 425-447. | Zbl | MR

[10] V.A. Galaktionov and S.A. Posashkov, Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations, Diff. Urav. 22, Vol. 7, 1986, pp. 1165-1173. | Zbl | MR

[11] V.A. Galaktionov, M.A. Herrero and J.J.L. Velázquez, The space structure near a blowup point for semilinear heat equations: of a formal approch, USSR Comput. Math. and Math. Physics, Vol. 31, 3, 1991, pp. 399-411. | Zbl | MR

[12] Y. Giga and R.V. Kohn, Asymptotically self similar blowup of semilinear heat equations, Comm. Pure Appli. Math., Vol. 38, 1985, pp. 297-319. | Zbl

[13] Y. Giga and R.V. Kohn, Characterising blow up using similarity variables, Indiana Univ. Math., Vol. 36, 1987, pp. 1-40. | Zbl

[14] Y. Giga and R.V. Kohn, Nondegeneracy of blowup for semilienear heat equations, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 297-319.

[15] M.A. Herrero and J.J.L. Velázquez, Blow-up Behaviour of One-Dimensional Semilinear Parabolic Equations, Ann. Inst. H. Poincaré, Anal. non linéaire, to appear. | Zbl | Numdam

[16] M.A. Herrero and J.J.L. Velázquez, Flat Blow-up in One-Dimensional Semilinear Parabolic Equations, Diff. and Integral Eqns., Vol. 5, 5, 1992, pp. 973-997. | Zbl

[17] M.A. Herrero and J.J.L. Velázquez, Blow-up Profiles in One-Dimensional Semilinear Parabolic Equations, Comm. P.D.E's, Vol. 17, 1992, pp. 205-219. | Zbl

[18] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag 1980. | Zbl

[19] O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Ural'Ceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Transl., American Mathematical Society, Providence, R.I., 1968. | Zbl

[20] W. Liu, Blowup Behavior for semilinear heat equations: multi-dimensional case, IMA preprint 711, Nov. 1990.

[21] F. Rellich, Perturbation theory of eigenvalue problems, Lecture Notes, New York University, 1953.

[22] J.J.L. Velázquez, Local behavior near blowup points for semilinear parabolic equations, J. Diff. Eqns., to appear. | Zbl

[23] J.J.L. Velázquez, Classification of singularities for blowing up solutions in higher dimensions, Trans. Amer. Math. Soc., to appear. | Zbl