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References
[AW] Acker, A., Walter, W.: The quenching problem for nonlinear parabolic differential equations. In: Everitt, W.M., Sleeman, B.D. (eds.) Ordinary and partial differential equations. Proceedings, Dundee 1976 (Lect. Notes Math., vol. 564, pp. 1–12) Berlin Heidelberg New York: Springer 1976
[AK] Acker, A., Kawohl, B.: Remarks on quenching. Nonlinear Anal.,13, 53–61 (1989)
[BB] Bandle, C., Brauner, C.: Singular perturbation method in a parabolic problem with free boundary. In: Godunov, S.K., Miller, J.J.H., Novikov, V.A. (eds.) Proceedings, BAIL IVth Conference, Novosibirsk, pp. 7–14. Dublin: Boole Press 1987
[BSS] Bandle, C., Sperb, R.P., Stakgold, I.: Diffusion and reaction with monotone kinetics. Nonlinear Anal.8, 321–333 (1984)
[BS] Bandle, C., Stakgold, I.: The formation of the dead core in parabolic reaction diffusion problems. Am. Math. Soc. Trans.286, 275–293 (1984)
[BC] Baras, P., Cohen, L.: Complete blow up afterT max for the solution of a semilinear heat equation. J. Funct. Anal.71, 142–174 (1987)
[BK] Berbernes, J.W., Kassoy, D.R.: A mathematical analysis of blow-up for thermal reactions — The spatially inhomogeneous case. SIAM J. Appl. Math.40, 476–485 (1981)
[CW] Chipot, M., Weissler, F.B.: Some blow up results for a nonlinear parabolic equation with a gradient term. SIAM J. Math. Anal. (in press)
[Fi] Fila, M.: Boundedness of global solutions of nonlinear diffusion equations. Preprint 497, SFB123, Heidelberg (1988)
[F] Friedman, A.: Blow up solutions of nonlinear evolution equations. In: Crandall, M.G., Rabinowitz, P.H., Turner, E.L. (eds.) Directions in paratial differential equations. pp. 75–88: New York London: Academic Press 1987
[FH] Friedman, A., Herrero, M.: Extinction properties of semilinear heat equations with strong absorption. J. Math. Anal. Appl.124, 530–546 (1987)
[FM] Friedman, A., McLeod, J.B.: Blow up of positive solutions of semilinear heat equations. Indiana Univ. Math. J.35, 425–447 (1985)
[GP] Galaktionov, V.A., Posashkov, S.A.: Exact solutions of parabolic equations with quadratic nonlinearities (in Russian), Preprint, Moscow, 1988
[GK] Giga, Y., Kohn, R.: Asymptotically self similar blow up of semilinear heat equations. Comm. Pure Appl. Math.38, 297–319 (1985)
[Ke] Kennington, A.: Convexity of level curves for an initial value problem. J. Math. Anal. Appl.13, 324–330 (1988)
[La] Lacey, A.: Global blow-up of a nonlinear heat equation. Proc. Roy. Soc. Edinburgh104A, 161–167 (1986)
[LM] Levine, H.A., Montgomery, J.T.: The quenching of solutions of some nonlinear parabolic equations. SIAM J. Math. Anal.11, 842–847 (1980)
[L] Lions, P.L.: On the existene of positive solutions of semilinear elliptic equations. SIAM Review24, 441–467 (1982)
[P] Phillips, D.: Existence of solutions to a quenching problem. Appl. Anal.24, 253–264 (1987)
[S1] Schaaf, R.: Global behaviour of solution branches for some Neumann problems depending on one or several parameters. J. Reine Angew. Math.346, 1–31 (1984)
[S2] Schaaf, R.: Global solution branches of two-point boundary value problems. Habilitationsschrift (1987) Heidelberg
[V] Vazquez, J.L.: A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optimization12, 191–202 (1984)
[W] Weissler, F.B.: Single point blow up for a semilinear initial value problem. J. Differ. Equations55, 204–224 (1984)
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Dedicated to Professor J. Hale on his 60th birthday
The results of this paper were announced at the Oberwolfach meeting on partial differential equations in June 1987
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Kawohl, B., Peletier, L.A. Observations on blow up and dead cores for nonlinear parabolic equations. Math Z 202, 207–217 (1989). https://doi.org/10.1007/BF01215255
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DOI: https://doi.org/10.1007/BF01215255