Rocky Mountain Journal of Mathematics

Blow-Up Behavior for Semilinear Heat Equations: Multi-Dimensional Case

Wenxiong Liu

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 23, Number 4 (1993), 1287-1319.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072494

Digital Object Identifier
doi:10.1216/rmjm/1181072494

Mathematical Reviews number (MathSciNet)
MR1256450

Zentralblatt MATH identifier
0801.35048

Subjects
Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35K55: Nonlinear parabolic equations 35K47

Keywords
Semilinear heat equations blow-up asymptotic behavior

Citation

Liu, Wenxiong. Blow-Up Behavior for Semilinear Heat Equations: Multi-Dimensional Case. Rocky Mountain J. Math. 23 (1993), no. 4, 1287--1319. doi:10.1216/rmjm/1181072494. https://projecteuclid.org/euclid.rmjm/1181072494


Export citation

References

  • J. Bebernes, D. Eberly, A description of self similar blow up for dimension $n\ge3$, Ann. Inst. H. Poincare Analyse Nonlineaire 5 (1988), 1-22.
  • X.Y. Chen, H. Matano and L. Veron, Anisotropic singularities of solutions of nonlinear elliptic equations in $R^2$, J. Funct. Anal. 83 (1989), 50-93.
  • S. Fillipas, Center manifold analysis for a semilinear parabolic equation arising in the study of the blowup of $u_t=\D u+u^p$, Ph.D. thesis, Courant Institute, New York University, 1990.
  • A. Friedman, Blow-up of solutions of nonlinear heat and wave equations, in Asymptotic analysis and numerical solutions of partial differential equations, to be published by Marcel Dekker.
  • A. Friedman and J.B. McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447.
  • H. Fujita, On the blowing-up of solutions of the Cauchy problem for $u_t=\D u+u^1+\a$, J. Fac. Sci. Univ. of Tokyo, Section I, 13 (1966), 109-124.
  • V.A. Galaktionov and S.A. Posashkov, The equation $u_t=u_xx+u^\b$, Localisation and asymptotic behavior of unbounded solutions, Preprint no. 97, Keldysh Institute of Applied Math., Moscow, 1985 (in Russian).
  • V.A. Galaktionov and S.A. Posashkov, Applications of a new comparison theorem to the study of unbounded solutions of nonlinear parabolic equations, Differ. Uranven 22 (1986), 1165-1173.
  • Y. Giga and R. Kohn, Asymptotically self similar blowup of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985), 297-319.
  • Y. Giga and R. Kohn, Characterizing blow up using similarity variables, Indiana Univ. Math. J. 36 (1987), 1-40.
  • Y. Giga and R. Kohn, Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math. 42 (1989), 297-319.
  • M.A. Herrero and J.J.L. Velázquez, Blow-up behavior of semilinear parabolic equations, Ann. Inst. H. Poincare Analyse Nonlineaire, to appear.
  • 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, RI, (1968).
  • W. Liu, The blowup rate of solutions of semilinear heat equations, J. Differ. Equations 77 (1989), 104-122.