On the Cauchy problem for a degenerate parabolic equation

Zeitschrift für Analysis und ihre Anwendungen

Volumn 20, Issue 3, 2001, Pages 677-690

  Winkler, M ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Degenerate diffusion; Large time behaviour

Indexed keywords

EID: 23044531603     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. N. Isr. J. Math. 47 (1984), 270-290.
2. Aronson, D. G.: The porous medium equation. Lect. Notes Math. 1224 (1986), 1-46.
3. Bandle, C. and H. Brunner: Blowup in diffusion equations: A survey. J. Comput. Appl. Math. 97 (1998), 3-22.
4. Bertsch, M., Kersner, R. and L. A. Peletier: Positivity versus localization in degenerate diffusion equations. Nonlin. Anal.: TMA 9 (1985), 987-1008.
5. Friedman, A. and B. McLeod: Blow-up of solutions of nonlinear degenerate parabolic equations. Arch. Rat. Mech. Anal. 96 (1987), 5-80.
6. Ladyzenskaja, O. A., Solonnikov, V.A. and N. N. Ural'ceva: Linear and Quasi-linear Equations of Parabolic Type. Providence (R.I., USA): Amer. Math. Soc. 1968.
7. N ; Nichtnegative Lösungen des Anfangswertproblems und ihre Asymptotik für große Zeiten. Diploma thesis. Bayreuth: Univ. 1990.
8. Tanabe, H.: Functional Analytic Methods for Partial Differential Equations. New York: Dekker 1997.
9. Wiegner, M.: Blow-up for solutions of some degenerate parabolic equations. Diff. Int. Eqns. 7 (1994), 1641-1647.
10. Wiegner, M.: A degenerate diffusion equation with a nonlinear source term. Nonlin. Anal.: TMA 28 (1997), 1977-1995.
11. Winkler, M.: Some Results on Degenerate Parabolic Equations not in Divergence Form. PhD Thesis. Aachen: RWTH Univ. 2000; www.math1.rwth-aachen.de/Forschung-Research/d_emath1.html.
12. Winkler, M.: A necessary and sufficient condition for blow-up of solutions of certain quasilinear parabolic equations. Preprint. Aachen 2000; www.math1.rwth-aachen.de/Forschung-Research/d.emath1.html.