@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}, volume = {10}, year = {1993}, pages = {313-344}, mrnumber = {1230711}, zbl = {0815.35039}, language = {en}, url = {http://dml.mathdoc.fr/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) pp. 313-344. http://gdmltest.u-ga.fr/item/AIHPC_1993__10_3_313_0/
[1] Final Time Blowup Profiles For Semilinear Parabolic Equations Via Center Manifold Theory, preprint. | MR 1166561
and ,[2] 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
and ,[3] 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
and ,[4] Stable Blow-up Patterns, J. Diff. Eqns., Vol. 98, 1992, pp. 947-960. | MR 1168971 | Zbl 0770.35010
,[5] 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
and ,[6] Applications of centre manifold theory, Springer-Verlag, New York, 1981. | MR 635782 | Zbl 0464.58001
,[7] Refined Asymptotic for the blowup of ut - Δu = up, Comm. Pure Appl. Math., Vol. 45, 1992, pp. 821-869. | MR 1164066 | Zbl 0784.35010
and ,[8] Blow-up of Solutions of Nonlinear Heat and Wave Equations, prcprint.
,[9] Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J., Vol. 34, 1985, pp. 425-447. | MR 783924 | Zbl 0576.35068
and ,[10] 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
and ,[11] 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
, and ,[12] Asymptotically self similar blowup of semilinear heat equations, Comm. Pure Appli. Math., Vol. 38, 1985, pp. 297-319. | Zbl 0585.35051
and ,[13] Characterising blow up using similarity variables, Indiana Univ. Math., Vol. 36, 1987, pp. 1-40. | Zbl 0601.35052
and ,[14] Nondegeneracy of blowup for semilienear heat equations, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 297-319.
and ,[15] Blow-up Behaviour of One-Dimensional Semilinear Parabolic Equations, Ann. Inst. H. Poincaré, Anal. non linéaire, to appear. | Numdam | Zbl 0813.35007
and ,[16] Flat Blow-up in One-Dimensional Semilinear Parabolic Equations, Diff. and Integral Eqns., Vol. 5, 5, 1992, pp. 973-997. | Zbl 0767.35036
and ,[17] Blow-up Profiles in One-Dimensional Semilinear Parabolic Equations, Comm. P.D.E's, Vol. 17, 1992, pp. 205-219. | Zbl 0772.35027
and ,[18] Perturbation Theory for Linear Operators, Springer-Verlag 1980. | Zbl 0435.47001
,[19] Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Transl., American Mathematical Society, Providence, R.I., 1968. | Zbl 0174.15403
, and ,[20] Blowup Behavior for semilinear heat equations: multi-dimensional case, IMA preprint 711, Nov. 1990.
,[21] Perturbation theory of eigenvalue problems, Lecture Notes, New York University, 1953.
,[22] Local behavior near blowup points for semilinear parabolic equations, J. Diff. Eqns., to appear. | Zbl 0798.35023
,[23] Classification of singularities for blowing up solutions in higher dimensions, Trans. Amer. Math. Soc., to appear. | Zbl 0803.35015
,