Quasilinear degenerate evolution equations in Banach spaces

Journal of Evolution Equations

Volumn 4, Issue 3, 2004, Pages 421-449

  Favini, Angelo ^a   Yagi, Atsushi ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

Degenerate quasilinear equations; Parabolic elliptic equations

Indexed keywords

EID: 4444318875     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-004-0169-4     Document Type: Article

References (17)

1. BARDOS, C. and BREZIS, H., Sur une classe de problèmes d'évolution nonlinéaires, J. Diff. Eqs. 6 (1969), 345-394.
2. BREZIS, H., On some degenerate nonlinear parabolic equations, Nonlinear Functional Analysis. Proc. Symp. Pure Math. 18 (1970), 28-38.
3. FAVINI, A. and YAGI, A., Multivalued linear operators and degenerate evolution equations, Ann. Mat. Pura. Appl. (IV) 163 (1993), 353-384.
4. P-approach to singular linear parabolic equations in bounded domains, Preprint.
5. KUTTLER, A., A degenerate nonlinear Cauchy problem, Applicable Analysis 13 (1982), 307-322.
6. KUTTLER, A., Implicit evolution equations, Appl. An. 16 (1983), 91-99.
7. OSAKI, K., TSUJIKAWA, T., YAGI, A. and MIMURA, M., Exponential attractor for a chemotaxis-growth system of equations, Nonlinear Analysis 51 (2002), 119-144.
8. SOBOLEVSKII, P. E., Equations of parabolic type in Banach space, Amer. Math. Soc. Trans. Ser. 2. 49 (1966), 1-62.
9. YAGI, A., Abstract quasilinear evolution equations of parabolic type in Banach spaces, Boll. Un. Mat. Ital. 5-B (1991), 341-368.
10. CARROLL, R. W. and SHOWALTER, R. E., Singular and Degenerate Cauchy Problems, 1976, Academic Press, London, New York.
11. FAVINI, A. and YAGI, A., Degenerate Differential Equations in Banach Spaces, 1999, Marcel Dekker, New York.
12. FRIEDMAN, A., Partial Differential Equations, 1969, Holt, Rinehart and Winston, New York.
13. LIONS, J. L. et MAGENES, E., Problèmes aux limites non homogènes et Applications, vol. 1, 1968, Dunod, Paris.
14. RABOTNOV, YU. N., Polzuchest' Elementov Konstruktsii (Creep of constructional elements), 1967, Nauka, Moscow.
15. SHOCKLEY, W., Electrons and Holes in Semiconductors, 1950, D. Van Nostrand, Princeton, New Jersey.
16. SHOWALTER, R. E., Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Math. Surveys & Monographs 49, 1997, AMS, Providence.
17. TANABE, H., Functional Analytic Methods for Partial Differential Equations, 1997, Marcel Dekker, New York.