Highly degenerate quasilinear parabolic systems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 18 (1991) no. 1, p. 135-166
@article{ASNSP_1991_4_18_1_135_0,
author = {Amann, Herbert},
title = {Highly degenerate quasilinear parabolic systems},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 18},
number = {1},
year = {1991},
pages = {135-166},
zbl = {0738.35029},
mrnumber = {1118224},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1991_4_18_1_135_0}
}

Amann, Herbert. Highly degenerate quasilinear parabolic systems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 18 (1991) no. 1, pp. 135-166. http://www.numdam.org/item/ASNSP_1991_4_18_1_135_0/

[1] H. Amann, Semigroups and nonlinear evolution equations, Linear Algebra Appl. 84 (1986), 3-32. | MR 872274 | Zbl 0624.35047

[2] H. Amann, On abstract parabolic fundamental solutions, J. Math. Soc. Japan 39 (1987), 93-116. | MR 867989 | Zbl 0616.47032

[3] H. Amann, Dynamic theory of quasilinear parabolic equations - I. Abstract evolution equations, Nonlinear Anal., Theory, Methods & Appl. 12 (1988), 895-919. | MR 960634 | Zbl 0666.35043

[4] H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differential Equations 72 (1988), 201-270. | MR 932367 | Zbl 0658.34011

[5] H. Amann, Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems, Differential Integral Equations 3 (1990), 13-75. | MR 1014726 | Zbl 0729.35062

[6] H. Amann, Dynamic theory of quasilinear parabolic systems - III. Global existence, Math. Z. 202 (1989), 219-250. | MR 1013086 | Zbl 0702.35125

[7] H. Amann, Erratum, Math. Z. 205 (1990), 331. | MR 1076139 | Zbl 0719.35044

[8] H. Amann, Global existence for a class of highly degenerate parabolic systems, Japan J. Industrial Appl. Math. (to appear). | MR 1093833 | Zbl 0735.35080

[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). | MR 1132018 | Zbl 0780.35051

[10] H. Amann, Substitution operators in Besov spaces, (to appear).

[11] J. Bergh - J. Löfström, Interpolation Spaces, An Introduction, Springer Verlag, Berlin, 1976. | MR 482275 | Zbl 0344.46071

[12] Ph. Clément - H.J.A.M. Heijmans et al., One-Pärameter Semigroups, CWI Monographs 5, North-Holland, Amsterdam, 1987. | MR 915552 | Zbl 0636.47051

[13] D.S. Cohen - R.W. Cox, A mathematical model for stress-driven diffusion in polymers, J. Polymer Science, Part B: Polymer Physics 27 (1989), 589-602.

[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 Physics 27 (1989), 1731-1747.

[15] D.S. Cohen - A.B. White Jr., Sharp fronts due to diffusion and viscoelastic relaxation in polymers, SIAM J. Appl. Math. (to appear). | MR 1095029 | Zbl 0718.76095

[16] R.W. Cox, A model for stress-driven diffusion in polymers, Ph.D. thesis, Dept. Appl. Math., California Institute of Technology, (1988).

[17] R.W. Cox, Stress-assisted diffusion: a free boundary problem, (to appear). | MR 1135996

[18] K.-J. Engel, Polynomial operator matrices as semigroup generators: the 2 × 2 case, Math. Ann. 284 (1989), 563-576. | MR 1006372 | Zbl 0652.34013

[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. | MR 216336 | Zbl 0154.16201

[20] P. Grisvard, Équations différentielles abstraites, Ann. Sci. École Norm. Sup., (4), 2 (1969), 311-395. | Numdam | MR 270209 | Zbl 0193.43502

[21] D. Guidetti, On interpolation with boundary conditions, (to appear). | MR 1115176

[22] T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad. 35 (1959), 467-468. | MR 117570 | Zbl 0095.10502

[23] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, New York, 1966. | MR 203473 | Zbl 0148.12601

[24] M.A. Krasnoselskii - P.P. Zabreiko - E.I. Pustylnik - P.E. Sobolevski, Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden, 1976. | MR 385645

[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. | MR 912310 | Zbl 0646.47045

[26] R. Nagel, Towards a "matrix theory" for unbounded operator matrices, Math. Z. 201 (1989), 57-68. | MR 990188 | Zbl 0672.47001

[27] R. Seeley, Norms and domains of the complex powers Az B, Amer. J. Math. 93 (1971), 299-309. | MR 287376 | Zbl 0218.35034

[28] R. Seeley, Interpolation in Lp with boundary conditions, Stud. Math. Appl. XLIV (1972), 47-60. | MR 315432 | Zbl 0237.46041

[29] E. Sinestrari, On the abstract Cauchy problems of parabolic type in spaces of continuous functions, J. Math. Anal. Appl. 107 (1985), 16-66. | Zbl 0589.47042

[30] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam, 1978. | Zbl 0387.46032