Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state

Philippe Souplet; Fred B Weissler

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 2, page 213-235
  • ISSN: 0294-1449

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Souplet, Philippe, and Weissler, Fred B. "Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state." Annales de l'I.H.P. Analyse non linéaire 20.2 (2003): 213-235. <http://eudml.org/doc/78577>.

@article{Souplet2003,
author = {Souplet, Philippe, Weissler, Fred B},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {profile equation; existence, uniqueness and asymptotic behavior},
language = {eng},
number = {2},
pages = {213-235},
publisher = {Elsevier},
title = {Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state},
url = {http://eudml.org/doc/78577},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Souplet, Philippe
AU - Weissler, Fred B
TI - Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 2
SP - 213
EP - 235
LA - eng
KW - profile equation; existence, uniqueness and asymptotic behavior
UR - http://eudml.org/doc/78577
ER -

References

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  1. [1] Cazenave T., Weissler F.B., Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z.228 (1998) 83-120. Zbl0916.35109MR1617975
  2. [2] Dohmen C., Hirose M., Structure of positive radial solutions to the Haraux–Weissler equation, Nonlinear Anal. TMA33 (1998) 51-69. Zbl0934.34028MR1623045
  3. [3] Galaktionov V.A., Vazquez J.L., Continuation of blowup solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math.50 (1997) 1-67. Zbl0874.35057MR1423231
  4. [4] Haraux A., Weissler F.B., Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J.31 (1982) 167-189. Zbl0465.35049MR648169
  5. [5] Joseph D.D., Lundgren T.S., Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal.49 (1973) 241-269. Zbl0266.34021MR340701
  6. [6] Peletier L.A., Terman D., Weissler F.B., On the equation Δu+1/2, Arch. Rat. Mech. Anal.94 (1986) 83-99. Zbl0615.35034
  7. [7] Vazquez J.L., Domain of existence and blowup for the exponential reaction-diffusion equation, Indiana Univ. Math. J.48 (1999) 677-709. Zbl0928.35080MR1722813
  8. [8] Weissler F.B., Asymptotic analysis of an ordinary differential equation and non-uniqueness for a semilinear partial differential equation, Arch. Rat. Mech. Anal.91 (1986) 231-245. Zbl0614.35043MR806003
  9. [9] Weissler F.B., Lp-energy and blow-up for a semilinear heat equation, Proc. Symp. Pure Math. Part II45 (1986) 545-551. Zbl0631.35049MR843641
  10. [10] Yanagida E., Uniqueness of rapidly decaying solutions of the Haraux–Weissler equation, J. Differential Equations127 (1996) 561-570. Zbl0856.34058MR1389410

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