×

zbMATH — the first resource for mathematics

The linearization principle for the stability of solutions of quasilinear parabolic equations. I. (English) Zbl 0497.35006

MSC:
35B35 Stability in context of PDEs
35K55 Nonlinear parabolic equations
47H20 Semigroups of nonlinear operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] S. Agmon: On the Eigenfunctions and the Eigenvalues of General Elliptic Boundary Value Problems. Comm. Pure Appl. Math. 15 (1962) pp. 119-147. · Zbl 0109.32701
[2] F. E. Browder: On the Spectral Theory of Elliptic Differential Operators. I. Math. Ann. 142 (1961) pp. 22-130. · Zbl 0104.07502
[3] P. L. Butzer & H. Berens: Semigroups of Operators and Approximation. Springer, Berlin (1967).
[4] G. da Prato & P. Grisvard: Sommes d’opérateurs linéaires et équations différentielles opérationnelles. Journ. Math. Pures et Appl. 54 (1975) pp. 305-387. · Zbl 0315.47009
[5] G. da Prato & P. Grisvard: Equations d’évolution abstraites non linéaires de type parabolique. C. Rend. Acad. Sc. Paris 283, Ser A (1976) pp. 709-711. · Zbl 0356.35048
[6] J. Dieudonne: Fondements de l’analyse moderne. Gauthier-Villars, Paris (1968).
[7] P. Grisvard: Caractérisation de quelques espaces d’interpolation. Arch. Rational Mech. Anal. 25 (1967) pp. 40-63. · Zbl 0187.05901
[8] T. Kato: Abstract Evolution Equations of Parabolic Type in Banach spaces. Nagoya Math. J. 19 (1961) pp. 93-125. · Zbl 0114.06102
[9] T. Kato: Perturbation Theory for Linear Operators. Springer, Berlin (1966). · Zbl 0148.12601
[10] T. Kato & H. Tanabe: On the Abstract Evolution Equation. Osaka Math. J. 14 (1962) pp. 107-133. · Zbl 0106.09302
[11] H. Kielhöfer: Stability and Semilinear Evolution Equations in Hilbert Space. Arch. Rational Mech. Anal. 57 (1974) pp. 150-165.
[12] H. Kielhöfer: Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme. Math. Z. 142 (1975) pp. 131-166. · Zbl 0324.35047
[13] H. Kielhöfer: On the Lyapunov-Stability of Stationary Solutions of Semilinear Parabolic Differential Equation. Journ. Diff. Equat. 22 (1976) pp. 193-208. · Zbl 0341.35049
[14] M.A. Krasnoselskii et al.: Integral Operators in Spaces of Summable Functions. Noordhoff, Leyden (1976).
[15] J. L. Lions & J. Peetre: Sur une classe d’espaces d’interpolation. Publ. Math, de l’I.H.E.S. 19 (1964).
[16] J. Peetre: Espaces d’interpolation et théorèmes de Sobolev. Ann. Inst. Fourier 16 (1966) pp. 279-317. · Zbl 0151.17903
[17] M. Potier-Ferry: Thèse, Paris (1978).
[18] M. Potier-Ferry: An Existence and Stability Theorem in Nonlinear Viscoelasticity. in ?Variational Methods in the Mechanics of Solids?, S. Nemat-Nasser, Ed., Pergamon Press, Oxford (1980) pp. 327-331.
[19] M. Potier-Ferry: On the Mathematical Foundations of Elastic Stability Theory, I To appear in Arch. Rational Mech. Anal. 78 (1982). · Zbl 0488.73043
[20] S. L. Sobolev: Applications of Functional Analysis in Mathematical Physics. Amer. Math. Soc., Providence (1963).
[21] P. E. Sobolevskii: Equations of Parabolic Type in Banach spaces. Amer. Math. Soc. Transl. 49 (1966) pp. 1-62.
[22] Y. Ebihara: J. Math. Pure Appl. 58 (1979).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.