Regularity of the solutions of second order evolution equations and their attractors
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 14 (1987) no. 3, pp. 485-511.
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     title = {Regularity of the solutions of second order evolution equations and their attractors},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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}
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Ghidaglia, J. M.; Temam, R. Regularity of the solutions of second order evolution equations and their attractors. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 14 (1987) no. 3, pp. 485-511. http://archive.numdam.org/item/ASNSP_1987_4_14_3_485_0/

[1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12 (1959), 623-727. | MR | Zbl

[2] A.V. Babin and M.I. Vishik, Regular attractors of semigroups and evolution equations, J. Math Pures Appl., 62 (1983), 441-491. | MR | Zbl

[3] A.V. Babin et M.I. Vishik, Attracteurs maximaux dans les équations aux dérivées partielles, Séminaire du Collège de France, J.L. Lions Ed., Pitman, Boston, 1985. | MR | Zbl

[4] C. Bardos, A regularity theorem for parabolic equations, J. Funct. Anal., 7 (1971), 311-322. | MR | Zbl

[5] L. Comtet, Advanced Combinatorics, D. Reidel, Dordrecht, 1978. | Zbl

[6] N. Dunford and J. Schwartz, Linear Operators Part II, Self adjoint Operators in Hilbert Spaces, Interscience Publishers, 1963. | Zbl

[7] H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR | Zbl

[8] J.M. Ghidagua and R. Temam, Attractors for damped nonlinear hyperbolic equations, J. Math. Pures et Appl., 66(3) 1987, pp. 273-319, and C.R. Acad. Sci. Paris. t. 300, série I, n° 7, 1985, pp. 185-188. | MR | Zbl

[9] J.M. Ghidaglia and R. Temam, Dimension of the universal attractor describing time periodically driven Sine-Gordon equation, Transport Theory and Statistical Physics, 16, 1987, pp. 253-265. | MR | Zbl

[10] J. Hale, Asymptotic behavior and dynamics in infinite dimensions, Lectures in Granada, Pitman, Boston, 1985. | MR | Zbl

[11] J.K. Hale and J. Scheurle, Smoothness of bounded solutions of nonlinear evolution equations, J. Differential Equations, 56 (1985), 142-163. | MR | Zbl

[12] A. Haraux, Two remarks on dissipative hyperbolic problems, Séminaire du Collège de France, J.L. Lions Ed., Pitman, Boston, 1985. | MR

[13] O.A. Ladyzhenksaya, V.A. Solonikov and N.N. Ural, Linear and quasilinear equations of parabolic type, Translation of Math. Monographs, n° 23, Amer. Math. Soc., Providence R.I.

[14] N. Levinson, Transformation theory of nonlinear differential equations of the second order, Annals of Math., 45, 4, (1944), 723-737. | MR | Zbl

[15] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. | MR | Zbl

[16] J.L. Lions and E. Magenes, Nonhomogeneous boundary value problems and applications, Springer, Berlin, 1972 (translated from Dunod, Paris, 1968). | Zbl

[17] J.L. Lions and W.A. Strauss, Some nonlinear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96. | Numdam | MR | Zbl

[18] B. Mandelbrot, Fractals: Form, Chance and Dimension, Freeman, San Francisco, 1977. | MR | Zbl

[19] J.B. Rauch and F. Masseyiii, Differentiability of solutions to hyperbolic initial-boundary value problem, Trans. Amer. Math. Soc., 189 (1974), 303-318. | MR | Zbl

[20] J. Sather, The existence of global classical solution of the initial-boundary value problem for □ u + u3 = f. Arch. Rational Mech. Anal., 22 (1966), 292-307. | Zbl

[21] I. Segal, Nonlinear semi-groups, Ann. of Math., 78, n° 2. 1963. | MR | Zbl

[22] J. Smale, Smooth solutions of the heat and wave equations, Comment. Math. Helvetici, 55 (1980), 1-12. | MR | Zbl

[23] R. Temam, Behaviour at time t = 0 of the solutions of semi-linear evolution equations, J. Differential Equations, 43 (1982), 73-92. | MR | Zbl

[24] J.M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Scient. Ecole Norm. Sup., 4e Série, 14 (1981), 209-246. | Numdam | MR | Zbl