Space and time regularity for degenerate evolution equations

Angelo FAVINI; Atsushi YAGI

doi:10.2969/jmsj/04420331

Angelo FAVINI, Atsushi YAGI

著者情報

ジャーナルフリー

1992 年 44 巻 2 号 p. 331-350

DOI https://doi.org/10.2969/jmsj/04420331

詳細

Published: 1992 Received: 1990/06/15 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) P. Acquistapace and B. Terreni, Some existence and regularity results for abstract non-autonomous parabolic equations, J. Math. Anal. Appl., 99 (1984), 9-64.
2) H. Brezis, On some degenerate nonlinear parabolic equations, Proc. Symp. Pure Math., 18, ed. AMS 1970, 28-38.
3) P. M. Brown, Constructive function-theoretic methods for fourth order pseudoparabolic and metaparabolic equations, Thesis, Indiana Univ., 1973.
4) G. Coppoletta, Abstract singular evolution equations of “hyperbolic” type, J. Funct. Anal., 50 (1983), 50-66.
5) A. Favini, Abstract potential operator and spectral methods for a class of degenerate evolution problems, J. Diff. Equat., 39 (1981), 212-225.
6) A. Favini, Degenerate and singular evolution equations in Banach space, Math. Ann., 273 (1985), 17-44.
7) A. Favini and P. Plazzi, On some abstract degenerate problems of parabolic type-1: The linear case, Nonlinear Axial., 12 (1988), 1017-1027.
8) A. Favini and P. Plazzi, On some abstract degenerate problems of parabolic type-3: Applications to linear and nonlinear problems, Osaka Math. J., 27 (1990), 323-359.
9) A. Favini and A. Yagi, Multivalued linear operators and degenerate evolution problems, to appear in Annali di Mat. Pura Appl.
10) A. Friedmann and Z. Schuss, Degenerate evolution equations in Hilbert Space, Trans. Amer. Math. Soc., 161 (1971), 401-427.
11) P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 5 (1972), 657-729.
12) R. E. Showalter, A nonlinear Sobolev equation, J. Math. Anal. Appl., 50 (1975), 183-190.
13) R. E. Showalter, Equations with operators forming a right angle, Pacific J. Math., 45 (1973), 357-362.
14) R. E. Showalter, Degenerate parabolic initial-boundary value problems, J. Diff. Equations, 31 (1979), 296-312.
15) E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., 107 (1985), 16-66.
16) R. W. Carroll and R. E. Showalter, Singular and degenerate Cauchy problems, ed. Academic Press, 1976.
17) E. Grepentrog and R. März, Differential-algebraic equations and their numerical treatment, ed. Teubner, 1986.
18) R. H. Martin, Jr., Nonlinear operators and differential equations in Banach spaces, ed. J. Wiley & Sons, 1976.
19) H. Tanabe, Equations of evolution, ed. Pitman, 1979.
20) K. Yosida, Functional analysis, ed. Springer, 1966.

Right : [1] P. Acquistapace and B. Terreni, Some existence and regularity results for abstract non-autonomous parabolic equations, J. Math. Anal. Appl., 99 (1984), 9-64.
[2] H. Brezis, On some degenerate nonlinear parabolic equations, Proc. Symp. Pure Math., 18, ed. AMS 1970, 28-38.
[3] P. M. Brown, Constructive function-theoretic methods for fourth order pseudoparabolic and metaparabolic equations, Thesis, Indiana Univ., 1973.
[4] G. Coppoletta, Abstract singular evolution equations of “hyperbolic” type, J. Funct. Anal., 50 (1983), 50-66.
[5] A. Favini, Abstract potential operator and spectral methods for a class of degenerate evolution problems, J. Diff. Equat., 39 (1981), 212-225.
[6] A. Favini, Degenerate and singular evolution equations in Banach space, Math. Ann., 273 (1985), 17-44.
[7] A. Favini and P. Plazzi, On some abstract degenerate problems of parabolic type-1: The linear case, Nonlinear Anal., 12 (1988), 1017-1027.
[8] A. Favini and P. Plazzi, On some abstract degenerate problems of parabolic type-3: Applications to linear and nonlinear problems, Osaka Math. J., 27 (1990), 323-359.
[9] A. Favini and A. Yagi, Multivalued linear operators and degenerate evolution problems, to appear in Annali di Mat. Pura Appl.
[10] A. Friedmann and Z. Schuss, Degenerate evolution equations in Hilbert Space, Trans. Amer. Math. Soc., 161 (1971), 401-427.
[11] P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 5 (1972), 657-729.
[12] R. E. Showalter, A nonlinear Sobolev equation, J. Math. Anal. Appl., 50 (1975), 183-190.
[13] R. E. Showalter, Equations with operators forming a right angle, Pacific J. Math., 45 (1973), 357-362.
[14] R. E. Showalter, Degenerate parabolic initial-boundary value problems, J. Diff. Equations, 31 (1979), 296-312.
[15] E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., 107 (1985), 16-66.
[16] R. W. Carroll and R. E. Showalter, Singular and degenerate Cauchy problems, ed. Academic Press, 1976.
[17] E. Grepentrog and R. März, Differential-algebraic equations and their numerical treatment, ed. Teubner, 1986.
[18] R. H. Martin, Jr., Nonlinear operators and differential equations in Banach spaces, ed. J. Wiley & Sons, 1976.
[19] H. Tanabe, Equations of evolution, ed. Pitman, 1979.
[20] K. Yosida, Functional analysis, ed. Springer, 1966.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）