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Singular solutions of the heat equation with absorption

Authors: S. Kamin and L. A. Peletier
Journal: Proc. Amer. Math. Soc. 95 (1985), 205-210
MSC: Primary 35K60
MathSciNet review: 801324
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Abstract: In this paper we prove that the source-type solutions converge-- when the total initial mass tends to infinity--to the very singular solution obtained in [3].

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  • [1] Haïm Brézis and Avner Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl. (9) 62 (1983), no. 1, 73–97. MR 700049
  • [2] Haïm Brézis and Elliott H. Lieb, Long range atomic potentials in Thomas-Fermi theory, Comm. Math. Phys. 65 (1979), no. 3, 231–246. MR 530151
  • [3] H. Brezis, L. A. Peletier, and D. Terman, A very singular solution of the heat equation with absorption, Arch. Rational Mech. Anal. 95 (1986), no. 3, 185–209. MR 853963, 10.1007/BF00251357
  • [4] Haïm Brézis and Laurent Véron, Removable singularities for some nonlinear elliptic equations, Arch. Rational Mech. Anal. 75 (1980/81), no. 1, 1–6. MR 592099, 10.1007/BF00284616
  • [5] S. Kamin and L. A. Peletier, Large time behavior of solutions of the heat equation with absorption, Ann. Scuola Norm. Sup. Pisa (to appear).
  • [6] O. A. Oleinik and S. N. Kruzhkov, Quasilinear second order parabolic equations with many independent variables, Russian Math. Surveys 16 (1961), 105-146.
  • [7] Laurent Véron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal. 5 (1981), no. 3, 225–242. MR 607806, 10.1016/0362-546X(81)90028-6
  • [8] Laurent Véron, Weak and strong singularities of nonlinear elliptic equations, Nonlinear functional analysis and its applications, Part 2 (Berkeley, Calif., 1983) Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 477–495. MR 843634

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Keywords: Singular solutions, source solutions, parabolic equations
Article copyright: © Copyright 1985 American Mathematical Society