Space and time regularity for degenerate evolution equations

Angelo FAVINI; Atsushi YAGI

doi:10.2969/jmsj/04420331

Angelo FAVINI, Atsushi YAGI

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1992 Volume 44 Issue 2 Pages 331-350

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

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Published: 1992 Received: June 15, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: 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.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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