Long-time vanishing properties of solutions of some semilinear parabolic equations

Yves Belaud; Bernard Helffer; Laurent Véron

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 1, page 43-68
  • ISSN: 0294-1449

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Belaud, Yves, Helffer, Bernard, and Véron, Laurent. "Long-time vanishing properties of solutions of some semilinear parabolic equations." Annales de l'I.H.P. Analyse non linéaire 18.1 (2001): 43-68. <http://eudml.org/doc/78512>.

@article{Belaud2001,
author = {Belaud, Yves, Helffer, Bernard, Véron, Laurent},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {quasilinear parabolic equations; Schrödinger operators; vanishing of solutions; semi-classical analysis; quenching},
language = {eng},
number = {1},
pages = {43-68},
publisher = {Elsevier},
title = {Long-time vanishing properties of solutions of some semilinear parabolic equations},
url = {http://eudml.org/doc/78512},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Belaud, Yves
AU - Helffer, Bernard
AU - Véron, Laurent
TI - Long-time vanishing properties of solutions of some semilinear parabolic equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 1
SP - 43
EP - 68
LA - eng
KW - quasilinear parabolic equations; Schrödinger operators; vanishing of solutions; semi-classical analysis; quenching
UR - http://eudml.org/doc/78512
ER -

References

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  7. 7 Gilbarg D, Trudinger N, Elliptic Partial Differential Equations of Second Order, Springer, 1977. Zbl0361.35003MR473443
  8. 8 Helffer B, Semi-classical analysis for the Schrödinger operator and applications, Lecture Notes in Math., Vol. 1336, Springer, 1989. Zbl0647.35002MR960278
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  10. 10 Kondratiev V, Véron L, Asymptotic behavior of the solutions of some parabolic or elliptic equations, Asymptotic AnalysisVol. 14 (1997) 117-156. Zbl0897.35013MR1451209
  11. 11 Laptev A, Netrusov Yu, On the negative eigenvalues of a class of Schrödinger operators, Preprint, KTH, Stockholm, 1998. Zbl0941.35055MR1730512
  12. 12 Lieb E.H, Thirring W, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relations to Sobolev inequalities, in: Studies in Math. Phys., Essays in Honour of V. Bargmann, Princeton Univ. Press, 1976. Zbl0342.35044
  13. 13 Lojaciewicz S, Ensembles Semi-Analytiques, Institut des Hautes Etudes Sci. Bures-sur-Yvette, France, 1964. 
  14. 14 Lojaciewicz S, Sur les ensembles semi-analytiques, in: Actes Congrès Intern. Math. 1970, Tome 2, 1971, pp. 237-241. Zbl0241.32005MR425152
  15. 15 Mazya V.G, Sobolev Spaces, Springer, 1985. Zbl0692.46023MR817985
  16. 16 Moser J, A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math.Vol. 13 (1960) 457-468. Zbl0111.09301MR170091
  17. 17 Nash J, Continuity of solutions of parabolic equations, Amer. J. Math.Vol. 80 (1958) 931-954. Zbl0096.06902MR100158
  18. 18 Rozenblyum G.V, Distribution of the discrete spectrum of singular differential operators, Doklady Akad. Nauk USSRVol. 202 (1972) 1012-1015. Zbl0249.35069MR295148
  19. 19 Whitney H, Local properties of analytic varieties, in: Cairns S.S (Ed.), Differential and Combinatorial Topology, 1965, pp. 205-244. Zbl0129.39402MR188486

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