Highly degenerate quasilinear parabolic systems

Herbert Amann

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)

  • Volume: 18, Issue: 1, page 135-166
  • ISSN: 0391-173X

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Amann, Herbert. "Highly degenerate quasilinear parabolic systems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18.1 (1991): 135-166. <http://eudml.org/doc/84092>.

@article{Amann1991,
author = {Amann, Herbert},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {operator theoretic method; existence theory; diffusion of penetrant on polymer entanglement network},
language = {eng},
number = {1},
pages = {135-166},
publisher = {Scuola normale superiore},
title = {Highly degenerate quasilinear parabolic systems},
url = {http://eudml.org/doc/84092},
volume = {18},
year = {1991},
}

TY - JOUR
AU - Amann, Herbert
TI - Highly degenerate quasilinear parabolic systems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1991
PB - Scuola normale superiore
VL - 18
IS - 1
SP - 135
EP - 166
LA - eng
KW - operator theoretic method; existence theory; diffusion of penetrant on polymer entanglement network
UR - http://eudml.org/doc/84092
ER -

References

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  1. [1] H. Amann, Semigroups and nonlinear evolution equations, Linear Algebra Appl.84 (1986), 3-32. Zbl0624.35047MR872274
  2. [2] H. Amann, On abstract parabolic fundamental solutions, J. Math. Soc. Japan39 (1987), 93-116. Zbl0616.47032MR867989
  3. [3] H. Amann, Dynamic theory of quasilinear parabolic equations - I. Abstract evolution equations, Nonlinear Anal., Theory, Methods & Appl.12 (1988), 895-919. Zbl0666.35043MR960634
  4. [4] H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differential Equations72 (1988), 201-270. Zbl0658.34011MR932367
  5. [5] H. Amann, Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems, Differential Integral Equations3 (1990), 13-75. Zbl0729.35062MR1014726
  6. [6] H. Amann, Dynamic theory of quasilinear parabolic systems - III. Global existence, Math. Z.202 (1989), 219-250. Zbl0702.35125MR1013086
  7. [7] H. Amann, Erratum, Math. Z.205 (1990), 331. Zbl0719.35044MR1076139
  8. [8] H. Amann, Global existence for a class of highly degenerate parabolic systems, Japan J. Industrial Appl. Math. (to appear). Zbl0735.35080MR1093833
  9. [9] H. Amann, Hopf bifurcation in quasilinear reaction-diffusion systems, in " Proceedings of the Claremont Conference on Differential Equations and Applications to Biology and Population Dynamics" (to appear). Zbl0780.35051MR1132018
  10. [10] H. Amann, Substitution operators in Besov spaces, (to appear). 
  11. [11] J. Bergh - J. Löfström, Interpolation Spaces, An Introduction, Springer Verlag, Berlin, 1976. Zbl0344.46071MR482275
  12. [12] PH. Clément - H.J.A.M. Heijmans et al., One-Pärameter Semigroups, CWI Monographs 5, North-Holland, Amsterdam, 1987. Zbl0636.47051MR915552
  13. [13] D.S. Cohen - R.W. Cox, A mathematical model for stress-driven diffusion in polymers, J. Polymer Science, Part B: Polymer Physics27 (1989), 589-602. 
  14. [14] D.S. Cohen - A.B. WhiteJr., Sharp fronts due to diffusion and stress at the glass transition in polymers, J. Polymer Science, Part B: Polymer Physics27 (1989), 1731-1747. 
  15. [15] D.S. Cohen - A.B. White Jr., Sharp fronts due to diffusion and viscoelastic relaxation in polymers, SIAM J. Appl. Math. (to appear). Zbl0718.76095MR1095029
  16. [16] R.W. Cox, A model for stress-driven diffusion in polymers, Ph.D. thesis, Dept. Appl. Math., California Institute of Technology, (1988). 
  17. [17] R.W. Cox, Stress-assisted diffusion: a free boundary problem, (to appear). Zbl0752.35089MR1135996
  18. [18] K.-J. Engel, Polynomial operator matrices as semigroup generators: the 2 × 2 case, Math. Ann.284 (1989), 563-576. Zbl0652.34013MR1006372
  19. [19] D. Fujiwara, Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order, Proc. Japan. Acad.43 (1967), 82-86. Zbl0154.16201MR216336
  20. [20] P. Grisvard, Équations différentielles abstraites, Ann. Sci. École Norm. Sup., (4), 2 (1969), 311-395. Zbl0193.43502MR270209
  21. [21] D. Guidetti, On interpolation with boundary conditions, (to appear). Zbl0713.46048MR1115176
  22. [22] T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad.35 (1959), 467-468. Zbl0095.10502MR117570
  23. [23] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, New York, 1966. Zbl0148.12601MR203473
  24. [24] M.A. Krasnoselskii - P.P. Zabreiko - E.I. Pustylnik - P.E. Sobolevski, Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden, 1976. MR385645
  25. [25] A. Lunardi, On the local dynamical system associated to a fully nonlinear abstract parabolic equation, in "Nonl. Anal. and Appl.", ed. V. Lakshmikantham, M. Decker, New York, 1987, 319-326. Zbl0646.47045MR912310
  26. [26] R. Nagel, Towards a "matrix theory" for unbounded operator matrices, Math. Z.201 (1989), 57-68. Zbl0672.47001MR990188
  27. [27] R. Seeley, Norms and domains of the complex powers Az B, Amer. J. Math.93 (1971), 299-309. Zbl0218.35034MR287376
  28. [28] R. Seeley, Interpolation in Lp with boundary conditions, Stud. Math. Appl.XLIV (1972), 47-60. Zbl0237.46041MR315432
  29. [29] E. Sinestrari, On the abstract Cauchy problems of parabolic type in spaces of continuous functions, J. Math. Anal. Appl.107 (1985), 16-66. Zbl0589.47042
  30. [30] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam, 1978. Zbl0387.46032

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