On the blowup of multidimensional semilinear heat equations
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 3, p. 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},
     publisher = {Gauthier-Villars},
     volume = {10},
     number = {3},
     year = {1993},
     pages = {313-344},
     zbl = {0815.35039},
     mrnumber = {1230711},
     language = {en},
     url = {http://http://www.numdam.org/item/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. http://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 1166561

[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. | Numdam | MR 936887 | Zbl 0726.35018

[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. | MR 948774 | Zbl 0652.65070

[4] A. Bressan, Stable Blow-up Patterns, J. Diff. Eqns., Vol. 98, 1992, pp. 947-960. | MR 1168971 | Zbl 0770.35010

[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. | MR 986159 | Zbl 0692.35013

[6] J. Carr, Applications of centre manifold theory, Springer-Verlag, New York, 1981. | MR 635782 | Zbl 0464.58001

[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. | MR 1164066 | Zbl 0784.35010

[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. | MR 783924 | Zbl 0576.35068

[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. | MR 853803 | Zbl 0632.35028

[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. | MR 1107061 | Zbl 0747.35014

[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 0585.35051

[13] Y. Giga and R.V. Kohn, Characterising blow up using similarity variables, Indiana Univ. Math., Vol. 36, 1987, pp. 1-40. | Zbl 0601.35052

[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. | Numdam | Zbl 0813.35007

[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 0767.35036

[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 0772.35027

[18] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag 1980. | Zbl 0435.47001

[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 0174.15403

[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 0798.35023

[23] J.J.L. Velázquez, Classification of singularities for blowing up solutions in higher dimensions, Trans. Amer. Math. Soc., to appear. | Zbl 0803.35015