Search and download archives of mathematical journals

 
 
  Table of contents for this issue | Next article
Herrero, M. A.; Velázquez, J. J. L.
Blow-up behaviour of one-dimensional semilinear parabolic equations. Annales de l'institut Henri Poincaré (C) Analyse non linéaire, 10 no. 2 (1993), p. 131-189
Full text djvu | pdf | Reviews MR 1220032 | Zbl 0813.35007 | 10 citations in Numdam

stable URL: http://www.numdam.org/item?id=AIHPC_1993__10_2_131_0

Bibliography

[A] S. Angenent, The Zero Set of a Solution of a Parabolic Equation, J. reine angew Math., Vol. 390, 1988, pp. 79-96.  MR 953678 |  Zbl 0644.35050
[AF] S.B. Angenent and B. Fiedler, The Dynamics of Rotating Waves in Scalar Reaction-Diffusion Equations, Trans. Amer. Math. Soc., Vol. 307, 1988, pp. 545-568.  MR 940217 |  Zbl 0696.35086
[AW] D.G. Aronson and H.F. Weinberger, Multidimensional Nonlinear Diffusion arising in Population Genetics, Advances in Math., Vol. 30, 1978, pp. 33-76.  MR 511740 |  Zbl 0407.92014
[BBE] J. Bebernes, A. Bressan and D. Eberly, A Description of Blow-up for the Solid Fuel Ignition Model, Indiana Univ. Math. J., Vol. 36, 1987, pp. 131-136.
[B] A. Bressan, On the Asymptotic Shape of Blow-up, Indiana Univ. Math. J., Vol. 39, 1990, pp. 947-960.  MR 1087180 |  Zbl 0798.35020
[CMV] X.Y. Chen, H. Matano and L. Veron, Anisotropic Singularities of Solutions of Nonlinear Elliptic Equations in R2, J. Funct. Anal., Vol. 83, 1989, pp. 50-93.  MR 993442 |  Zbl 0687.35020
[CL] P.J. Cohen and M. Lees, Asymptotic decay of Differential Inequalities, Pacific J. Math, Vol. 11, 1961, pp. 1235-1249.
Article |  MR 133601 |  Zbl 0171.35002
[D] J. Dold, Analysis of the Early Stage of Thermal Runaway, Quart. J. Mech. Appl. Math., Vol. 38, 1985, pp. 361-387.  Zbl 0569.76079
[FH] A. Friedman and J.B. McLeod, Blow-up of positive Solutions of Semilinear Heat Equations, Indiana Univ. Math. J., Vol. 34, 1985, pp. 425-447.  MR 783924 |  Zbl 0576.35068
[Fu] H. Fujita, On the Blowing-up of Solutions of the Cauchy Problem for ut = Δu + u1+α, J. Fac. Sci. Univ. of Tokio, Section I, Vol. 13, 1966, pp. 109-124.  MR 214914 |  Zbl 0163.34002
[GHV] V.A. Galaktionov, M.A. Herrero and J.J.L. Velázquez, The Space Structure near a Blow-up Point for Semilinear Heat Equations: a formal Approach, Soviet J. Comput. Math. and Math. Physics, Vol. 31, 1991, pp. 399-411.  MR 1107061 |  Zbl 0747.35014
[GP] V.A. Galakationov and S.A. Posashkov, Application of new Comparison Theorems in the Investigation of Unbounded Solutions of nonlinear Parabolic Equations, Diff. Urav., Vol. 22, 7, 1986, pp. 1165-1173.  MR 853803 |  Zbl 0632.35028
[GK1] Y. Giga and R.V. Kohn, Asymptotically Self-Similar Blow-up of Semilinear Heat Equations, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 297-319.  MR 784476 |  Zbl 0585.35051
[GK2] Y. Giga and R.V. Kohn, Characterizing Blow-up using Similarity Variables, Indiana Univ. Math., J., Vol. 36, 1987, pp. 1-40.  MR 876989 |  Zbl 0601.35052
[GK3] Y. Giga and R.V. Kohn, Nondegeneracy of Blow-up for Semilinear Heat Equations, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 845-884.  MR 1003437 |  Zbl 0703.35020
[H] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer Lecture Notes in Mathematics No. 840, 1981.  MR 610244 |  Zbl 0456.35001
[HV1] M.A. Herrero and J.J.L. Velázquez, Flat Blow-up in One-Dimensional Semilinear Heat Equations, Differential and Integral Equations, Vol. 5, 1992, pp. 973-997.  MR 1171974 |  Zbl 0767.35036
[L] A. A. LACEY, The Form of Blow-up for Nonlinear Parabolic Equations, Proc. Royal Soc. Edinburgh, Vol. 98 A, 1984, pp. 183-202.  MR 765494 |  Zbl 0556.35077
[La] P.D. Lax, A Stability Theorem for Solutions of Abstract Differential Equations, and its Application to the Study of the Local behaviour of Solutions of Elliptic Equations, Comm. Pure Appl. Math, Vol. 9, 1956, pp. 747-766.  MR 86991 |  Zbl 0072.33004
[Li] W. Liu, The Blow-up Rate of Solutions of Semilinear Heat Equations, J. Diff. Equations Vol. 77, 1989, pp. 104-122.  MR 980545 |  Zbl 0672.35035
[MW] C.E. Müller and F.B. Weissler, Single Point Blow-up for a General Semilinear Heat Equation, Indiana Univ. Math., J., Vol. 34, 1983, pp. 881-913.  MR 808833 |  Zbl 0597.35057
[W] F.B. Weissler, Single Point Blow-up of Semilinear Initial Value Problems, J. Diff. Equations, Vol. 55, 1984, pp. 204-224.  MR 764124 |  Zbl 0555.35061
[Wa] N.A. Watson, Parabolic Equations on an Infinite Strip, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 127, Marcel Dekker, 1988.  MR 988890 |  Zbl 0675.35001
[Wi] D.V. Widder, The Heat Equation, Academic Press, New York, 1975.  MR 466967 |  Zbl 0322.35041
Copyright Cellule MathDoc 2014 | Credit | Site Map