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Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions
Semigroup-theoretic approach to identification of linear diffusion coefficients
1. | Dipartimento di Matematica F. Brioschi, Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy |
2. | Department of Mathematics, Science University of Tokyo, 1-3 Kagurazaka, Sinjuku-ku, Tokyo 162-8601 |
3. | Institut für Mathematik, Martin-Luther Univ. Halle -Wittenberg, Theodor-Lieser-Strasse 506120 Halle (Saale), Germany |
4. | Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 |
References:
[1] |
H. Brezis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1983; (English Translation) Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, 2011. |
[2] |
P. Drábek and J. Milota, Methods of Nonlinear Analysis, Applications to Differential Equations, Advanced Texts, Birkhäuser Verlag, Basel, 2007. |
[3] |
J. Goldstein, Semigroups of Linear Operators and Applications, Oxford Math. Monograph, Clarendon Press, Oxford University Press, New York, 1985. |
[4] |
T. Kato, Perturbation Theory for Linear Operators, Grundlehren math. Wissenschften, 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976. |
[5] |
I. Miyadera, Nonlinear Semigroups, Translations of Math. Monograph 109, Amer. Math. Soc., Providence, RI, 1992. |
[6] |
G. Mola, Identification of the diffusion coefficient in linear evolution equations in Hilbert spaces, J. Abstr. Differ. Equ. Appl., 2 (2011), 14-28. |
[7] |
N. Okazawa, Sectorialness of second order elliptic operators in divergence form, Proc. Amer. Math. Soc., 113 (1991), 701-706.
doi: 10.1090/S0002-9939-1991-1072347-4. |
[8] |
E. M. Ouhabaz, Analysis of Heat Equations on Domains, London Mathematical Society Monographs Series, 31, Princeton Univ. Press, Princeton and Oxford, 2005. |
[9] |
A. L. Ruoff, Materials Science, Englewood Cliffs, N.J., Prentice-Hall, 1973. |
[10] |
J. Voigt, The sector of holomorphy for symmetric sub-Markovian semigroups, in Functional Analysis (Trier, 1994), de Gruyter, Berlin, 1996, 449-453. |
[11] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications. I. Fixed-point Theorems, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4612-4838-5. |
[12] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications. II/B. Nonlinear Monotone Operators, Springer-Verlag, New York, 1990.
doi: 10.1007/978-1-4612-0985-0. |
show all references
References:
[1] |
H. Brezis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1983; (English Translation) Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, 2011. |
[2] |
P. Drábek and J. Milota, Methods of Nonlinear Analysis, Applications to Differential Equations, Advanced Texts, Birkhäuser Verlag, Basel, 2007. |
[3] |
J. Goldstein, Semigroups of Linear Operators and Applications, Oxford Math. Monograph, Clarendon Press, Oxford University Press, New York, 1985. |
[4] |
T. Kato, Perturbation Theory for Linear Operators, Grundlehren math. Wissenschften, 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976. |
[5] |
I. Miyadera, Nonlinear Semigroups, Translations of Math. Monograph 109, Amer. Math. Soc., Providence, RI, 1992. |
[6] |
G. Mola, Identification of the diffusion coefficient in linear evolution equations in Hilbert spaces, J. Abstr. Differ. Equ. Appl., 2 (2011), 14-28. |
[7] |
N. Okazawa, Sectorialness of second order elliptic operators in divergence form, Proc. Amer. Math. Soc., 113 (1991), 701-706.
doi: 10.1090/S0002-9939-1991-1072347-4. |
[8] |
E. M. Ouhabaz, Analysis of Heat Equations on Domains, London Mathematical Society Monographs Series, 31, Princeton Univ. Press, Princeton and Oxford, 2005. |
[9] |
A. L. Ruoff, Materials Science, Englewood Cliffs, N.J., Prentice-Hall, 1973. |
[10] |
J. Voigt, The sector of holomorphy for symmetric sub-Markovian semigroups, in Functional Analysis (Trier, 1994), de Gruyter, Berlin, 1996, 449-453. |
[11] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications. I. Fixed-point Theorems, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4612-4838-5. |
[12] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications. II/B. Nonlinear Monotone Operators, Springer-Verlag, New York, 1990.
doi: 10.1007/978-1-4612-0985-0. |
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