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All issues Volume 26 (2020) ESAIM: COCV, 26 (2020) 126 References
Issue
ESAIM: COCV
Volume 26, 2020
Special issue in honor of Enrique Zuazua's 60th birthday
Article Number 126
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2020082
Published online 17 December 2020
  1. P. Baras and J. Goldstein, The heat equation with a singular potential. Trans. Am. Math. Soc. 284 (1984) 121–139. [Google Scholar]
  2. H. Brezis, Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York (2011). [Google Scholar]
  3. L. Caffarelli, R.V. Kohn and L. Nirenberg, First order interpolation inequalities with weights. Compositio Math. 53 (1984) 259–275. [Google Scholar]
  4. T. Cazenave, F. Dickstein, M. Escobedo and F.B. Weissler, Self-similar solutions of a nonlinear heat equation. J. Math. Sci. Univ. Tokyo 8 (2001) 501–540. [Google Scholar]
  5. T. Cazenave, F. Dickstein, I. Naumkin and F.B. Weissler, Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value. Am. J. Math. 142 (2020), 1439–1495. [CrossRef] [Google Scholar]
  6. T. Cazenave, F. Dickstein, I. Naumkin and F.B. Weissler, Perturbations of self-similar solutions. Dyn. Partial Differ. Equ. 16 (2019) 151–183. [CrossRef] [Google Scholar]
  7. M. Hoshino and E. Yanagida, Convergence rate to singular steady states in a semilinear parabolic equation. Nonlinear Anal. 131 (2016) 98–111. [CrossRef] [Google Scholar]
  8. T. Kato, Perturbation theory for linear operators, Reprint of the 1980 edition. Classics in Mathematics. Springer-Verlag, Berlin (1995). [CrossRef] [Google Scholar]
  9. G.M. Lieberman, Second order parabolic differential equations. World Scientific Publishing Co. Inc. River Edge, NJ (1996). [CrossRef] [Google Scholar]
  10. V.A. Liskevich and Z. Sobol, Estimates of integral kernels for semigroups associated with second-order elliptic operators with singular coefficients. Potential Anal. 18 (2003) 359–390. [CrossRef] [Google Scholar]
  11. R. Mazzeo and F. Pacard, A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis. J. Differential Geom. 44 (1996) 331–370. [CrossRef] [Google Scholar]
  12. P.D. Milman and Yu. A. Semenov, Heat kernel bounds and desingularizing weights. J. Funct. Anal. 202 (2003) 1–24. [Google Scholar]
  13. L. Moschini and A. Tesei, Parabolic Harnack inequality for the heat equation with inverse-square potential. Forum Math. 19 (2007) 407–427. [CrossRef] [Google Scholar]
  14. A. Pazy, Semi-groups of linear operators and applications to partial differential equations. Appl. Math. Sci. 44 (1983). [CrossRef] [Google Scholar]
  15. P. Quittner and P. Souplet, Superlinear parabolic problems. Blow-up, global existence and steady states. Second edition. Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser/Springer, Cham (2019). [CrossRef] [Google Scholar]
  16. S. Sato, Blow-up at space infinity of a solution with a moving singularity for a semilinear parabolic equation. Commun. Pure Appl. Anal. 10 (2011) 1225–1237. [CrossRef] [Google Scholar]
  17. S. Sato and E. Yanagida, Solutions with moving singularities for a semilinear parabolic equation. J. Differ. Equ. 246 (2009) 724–748. [Google Scholar]
  18. S. Sato and E. Yanagida, Forward self-similar solution with a moving singularity for a semilinear parabolic equation. Discrete Contin. Dynam. Syst. 26 (2010) 1313–1331. [CrossRef] [Google Scholar]
  19. S. Sato and E. Yanagida, Appearance of anomalous singularities in a semilinear parabolic equation. Commun. Pure Appl. Anal. 11 (2012) 387–405. [CrossRef] [Google Scholar]
  20. S. Sato and E. Yanagida, Asymptotic behavior of singular solutions for a semilinear parabolic equation. Discrete Contin. Dyn. Syst. 32 (2012) 4027–4043. [CrossRef] [Google Scholar]
  21. J. Serrin and H. Zou, Classification of positive solutions of quasilinear elliptic equations. Topol. Methods Nonlinear Anal. 3 (1994) 1–25. [Google Scholar]
  22. P. Souplet and F.B. Weissler, F.B.: Regular self-similar solutions to the nonlinear heat equation with initial data above the singular steady state. Ann. Inst. Henri Poincaré Anal. Non Linéaire 20 (2003) 213–235. [CrossRef] [Google Scholar]
  23. J.L. Vázquez and E. Vázquez, The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential. J. Funct. Anal. 173 (2000) 103–153. [Google Scholar]

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