A Cauchy problem for u t - Δ u = u p with 0 < p < 1 . Asymptotic behaviour of solutions

J. Aguirre; M. Escobedo

Annales de la Faculté des sciences de Toulouse : Mathématiques (1986-1987)

  • Volume: 8, Issue: 2, page 175-203
  • ISSN: 0240-2963

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Aguirre, J., and Escobedo, M.. "A Cauchy problem for $u_t - \Delta u = u^p \ \hbox{with}\ 0 &lt; p &lt; 1$. Asymptotic behaviour of solutions." Annales de la Faculté des sciences de Toulouse : Mathématiques 8.2 (1986-1987): 175-203. <http://eudml.org/doc/73195>.

@article{Aguirre1986-1987,
author = {Aguirre, J., Escobedo, M.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {existence; uniqueness; regularity; global solutions; Cauchy problem; self-similar solutions; asymptotic behaviour; nonlinear heat equation},
language = {eng},
number = {2},
pages = {175-203},
publisher = {UNIVERSITE PAUL SABATIER},
title = {A Cauchy problem for $u_t - \Delta u = u^p \ \hbox\{with\}\ 0 &lt; p &lt; 1$. Asymptotic behaviour of solutions},
url = {http://eudml.org/doc/73195},
volume = {8},
year = {1986-1987},
}

TY - JOUR
AU - Aguirre, J.
AU - Escobedo, M.
TI - A Cauchy problem for $u_t - \Delta u = u^p \ \hbox{with}\ 0 &lt; p &lt; 1$. Asymptotic behaviour of solutions
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1986-1987
PB - UNIVERSITE PAUL SABATIER
VL - 8
IS - 2
SP - 175
EP - 203
LA - eng
KW - existence; uniqueness; regularity; global solutions; Cauchy problem; self-similar solutions; asymptotic behaviour; nonlinear heat equation
UR - http://eudml.org/doc/73195
ER -

References

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  1. [1] Aronson ( D.G.) and Weinberger ( H.F.). — Multidimensional nonlinear diffusion arising in population genetics, Advances in Mathematics, t. 30, 1978, p. 33-76. Zbl0407.92014MR511740
  2. [2] Ekeland ( I.) and Temann ( R.).- Analyse Convexe et Problèmes Variationnels. Dunod, Paris, 1974. Zbl0281.49001
  3. [3] Escobedo ( M.) and Kavian ( O.).— Variational problems related to self-similar solutions of the heat equation. - to appear in J. of Nonlinear Analysis, Theory, Methods & Appl.. Zbl0639.35038
  4. [4] Escobedo ( M.) & Kavian ( O.) & Matano ( H.).- in preparation. 
  5. [5] Fujita ( H.).-On the blowing up of solutions of the Cauchy problem for ut = Δu + u1+α, J. Fac. Sci. Univ. of Tokio, Sect. I, t. 13, 1966, p. 109-124. Zbl0163.34002MR214914
  6. [6] Gmira ( A.) and Veron ( L.).— Large time bahaviour of the solutions of a semilinear parabolic equation in Rn, J. of Diff. Eq., t. 53, 1984, p. 259-276. Zbl0529.35041MR748242
  7. [7] Haraux ( A.) and Weissler ( F.B.).— Non uniqueness for a semilinear initial value problem, Indiana Univ. Math. J., t. 31, n°2, 1982, p. 167-189. Zbl0465.35049MR648169
  8. [8] Hayakawa ( K.). — On non-existence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., t. 49, 1973, p. 503-505. Zbl0281.35039MR338569
  9. [9] Kavian ( O.).— Remarks on the time behaviour of a non linear diffusion equation. Prépublication du Laboratoire d'Analyse Numérique, Universit, P. et M. Curie (Paris VI), 1985. 
  10. [10] Kobayashi ( K.), Sirao ( T.) and Tanaka ( H.).- On the growing up problem for semilinear heat equations, J. Math. Soc. Japan, t. 29, 1977, p. 407-424. Zbl0353.35057MR450783
  11. [11] Weissler ( F.B.).- Rapidly decaying solutions of an O.D.E. with applications to semilinear parabolic P.D.E.'s. - to appear. MR806004
  12. [12] Weissler ( F.B.).- Existence and non-existence of global solutions for a semilinear heat equation, Israel J. of Math., t. 38, n°1-2, 1981, p. 29-39. Zbl0476.35043MR554819

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