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Bertsch, M.; Peletier, L. A.

A positivity property of solutions of nonlinear diffusion equations. (English) Zbl 0488.35041

J. Differ. Equations 53, 30-47 (1984).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 13 Documents

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

Keywords:

nonnegative solution
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References:

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[2] Aronson, D. G.; Bénilan, Ph: Régularité des solutions de l’équation des milieux poreux dans RN. C. R. Acad. sci. Paris ser. A-B 288, 103-105 (1979) · Zbl 0397.35034
[3] Aronson, D. G.; Crandall, M. G.; Peletier, L. A.: Stabilization of a degenerate nonlinear diffusion problem. J. nonlinear anal. 6, 1001-1022 (1982) · Zbl 0518.35050
[4] Aronson, D. G.; Peletier, L. A.: Large time behaviour of solutions of the porous medium equation in bounded domains. J. differential equations 39, 378-412 (1981) · Zbl 0475.35059
[5] Bertsch, M.; Nanbu, T.; Peletier, L. A.: Decay of solutions of a nonlinear diffusion equation. J. nonlinear anal. 6, 539-554 (1982) · Zbl 0487.35051
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[8] Crandall, M. G.; Pierre, M.: Regularizing effects for \(ut + a{\phi}\) (u) = 0 in L1. J. funct. Anal. 45, 194-212 (1982) · Zbl 0483.35076
[9] Dafermos, C. M.: Asymptotic behaviour of solutions of evolution equations. Nonlinear evolution equations (1978) · Zbl 0499.35015
[10] Gurtin, M. E.; Maccamy, R. C.: On the diffusion of biological populations. Math. biosci. 33, 35-49 (1977) · Zbl 0362.92007
[11] Kalashnikov, A. S.: Nature of the propagation of perturbations in problems of nonlinear thermal conductivity with absorption. Zh. vychisl. Mati. mat. Fiz. 14, 891-905 (1974)
[12] Knerr, B. F.: The behaviour of the support of solutions of the equation of nonlinear heat conduction with absorption in one dimension. Trans. amer. Math. soc. 249, 409-424 (1979) · Zbl 0415.35045
[13] Oleinik, O. A.; Kalashnikov, A. S.; Yui-Lin, Chzou: The Cauchy problem and boundary problems for equations of the type of unsteady filtration. Izv. akad. Nauk SSR ser. Mat. 22, 667-704 (1958) · Zbl 0093.10302
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