A description of self-similar blow-up for dimensions n ≥ 3

J. Bebernes; D. Eberly

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 1, page 1-21
  • ISSN: 0294-1449

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Bebernes, J., and Eberly, D.. "A description of self-similar blow-up for dimensions $n \ge 3$." Annales de l'I.H.P. Analyse non linéaire 5.1 (1988): 1-21. <http://eudml.org/doc/78144>.

@article{Bebernes1988,
author = {Bebernes, J., Eberly, D.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {blow-up; initial-boundary value problem; semilinear parabolic equations; nonlinearities; asymptotic behaviour; self-similar solution; singular stationary solutions},
language = {eng},
number = {1},
pages = {1-21},
publisher = {Gauthier-Villars},
title = {A description of self-similar blow-up for dimensions $n \ge 3$},
url = {http://eudml.org/doc/78144},
volume = {5},
year = {1988},
}

TY - JOUR
AU - Bebernes, J.
AU - Eberly, D.
TI - A description of self-similar blow-up for dimensions $n \ge 3$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 1
SP - 1
EP - 21
LA - eng
KW - blow-up; initial-boundary value problem; semilinear parabolic equations; nonlinearities; asymptotic behaviour; self-similar solution; singular stationary solutions
UR - http://eudml.org/doc/78144
ER -

References

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  2. [2] J. Bebernes and D. Kassoy, A Mathematical Analysis of Blow-up for Thermal Reactions, S.I.A.M. J. Appl. Math., Vol. 40, 1981, pp. 476-484. Zbl0481.35048MR614744
  3. [3] J. Bebernes and W. Troy, On the Existence of Solutions to the Kassoy Problem in Dimension 1, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 1157-1162. Zbl0645.34008MR892494
  4. [4] H. Bellout, A Criterion for Blow-Up of Solutions to Semilinear Heat Equations, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 722-727. Zbl0645.35041MR883564
  5. [5] D. Eberly, On the Existence of Solutions to the Kassoy Problem on Dimensions 1 and 2, J. Math. Anal. Appl. (to appear). Zbl0659.34002MR924299
  6. [6] D. Eberly and W. Troy, On the Existence of Logarithmic-Type Solutions to the Kassoy Problem in Dimension 3, J. Differential Equations (to appear). Zbl0648.34018MR915490
  7. [7] A. Friedman and B. Mcleod, Blow-Up of Positive Solutions of Seminlinear Heat Equations, Indiana Univ. Math. J., Vol. 34, No. 2, 1985, pp. 425-447. Zbl0576.35068MR783924
  8. [8] Y. Giga and R.V. Kohn, Asymptotically Self-Similar Blow-Up of Semilinear Heat Equations, Comm. Pure and Appl. Math., Vol. 38, 1985, pp. 297-319. Zbl0585.35051MR784476
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  10. [10] W. Troy, The Existence of Bounded Solutions for a Semilinear Heat Equation, S.I.A.M. J. Math. Anal., Vol. 18, 1987, pp. 332-336. Zbl0655.35039MR876275
  11. [11] Y. Giga and R.V. Kohn, Characterizing Blowup Using Similarity Variables, Indiana Univ. Math. J., Vol. 36, 1987, pp. 1-40. Zbl0601.35052MR876989
  12. [12] V.A. Galaktionov and S.A. Posashkov, The Equation ut=uxx+uβ. Localization and Asymptotic Behavior of Unbounded Solutions, Diff. Uravnen, Vol. 22, 1986, pp. 1165-1173. 
  13. [13] Y. Giga, On Elliptic Equations Related to Self-Similar Solutions for Nonlinear Heat Equations, Hiroshima Math. J., Vol. 16, 1986, pp. 541-554. Zbl0626.35033MR867579
  14. [14] L.M. Hocking, K. Stewartson and J.T. Stuart, A Nonlinear Instability Burst in Plane Parallel Flow, J. Fluid Mech., Vol. 51, 1972, pp. 705-735. Zbl0232.76053
  15. [15] A. Kapila, Reactive-Diffusive Systems with Arrhenius Kinetics: Dynamics of Ignition, S.I.A.M. J. Appl. Math., Vol. 39, 1980, pp. 21-36. Zbl0489.76098MR585826
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