Evolution equations governed by families of weighted operators
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 3, p. 299-334
@article{AIHPC_1999__16_3_299_0,
     author = {Couchouron, J. F. and Ligarius, P.},
     title = {Evolution equations governed by families of weighted operators},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {3},
     year = {1999},
     pages = {299-334},
     zbl = {0926.34051},
     mrnumber = {1687282},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_3_299_0}
}
Couchouron, J. F.; Ligarius, P. Evolution equations governed by families of weighted operators. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 3, pp. 299-334. http://www.numdam.org/item/AIHPC_1999__16_3_299_0/

[1] P. Bénilan, Équations d'évolution dans un espace de Banach quelconque et applications, Thèse, Paris-XI, Orsay, 1972.

[2] Ph. Bénilan, M.G. Crandall and A. Pazy, Evolution equations governed by accretive operators, Book (to appear).

[3] J.M. Ball, J.E. Marsden and M. Slemrod, Controllability of distributed bilinear systems, Siam J. Control Optim., Vol. 20(6), 1982, pp. 575-597. | MR 661034 | Zbl 0485.93015

[4] H. Brezis, Analyse fonctionnelle - Théorie et applications, Masson, Paris, 1992. | MR 697382 | Zbl 0511.46001

[5] J.-F. Couchouron, Équations d'évolution: Le problème de Cauchy, Univ. de Rouen, Rouen, These, 1993.

[6] J.-F. Couchouron, Problème de Cauchy non autonome pour des équations d'évolution, à paraitre.

[7] J.-F. Couchouron and P. Ligarius, Weighted evolution equations and asymptotic observers in Banach spaces. A nonlinear approach, submitted.

[8] M.G. Crandall, Nonlinear semigroups and evolution governed by accretive operators, Proc. Sympos. in Pure Math., Vol. 45 (Part.I), 1986, pp. 305-337. | MR 843569 | Zbl 0637.47039

[9] M.G. Crandall and L.C. Evans, On the relation of the operator (∂/∂s) + (∂/∂τ) to evolution governed by accretive operators , Israël J. Math., Vol. 21 (4), 1975, pp. 261-278. | MR 390853 | Zbl 0351.34037

[10] M.G. Crandall and T.M. Liggett, Generation of semigroups of nonlinear transformations on general Banach spaces, American J. Math., Vol. 93, 1971, pp. 265-298. | MR 287357 | Zbl 0226.47038

[11] J. Diestel and J. Uhl Jr., Vector measure, Math. surveys - AMS, Vol. 15, 1977. | MR 453964 | Zbl 0369.46039

[12] L.C. Evans, Nonlinear evolution equations in an arbitrary Banach space, Israël J. Math., Vol. 26 (1), 1977, pp. 1-42. | MR 440431 | Zbl 0349.34043

[13] Hartman, Ordinary Differential Equations, J. Wiley & Sons 1964. | Zbl 0125.32102

[14] D. Hinrichsen and A.J. Pritchard, Robust stability of linear evolution operators on Banach spaces, Siam J. Control Optim., Vol. 32 (6), 1994, pp. 1503-1541. | MR 1297095 | Zbl 0817.93055

[15] K. Kobayasi, Y. Kobayashi and S. Oharu, Nonlinear evolution operators in Banach spaces, Osaka J. Math., Vol. 21, 1984, pp. 281-310. | MR 752464 | Zbl 0567.47047

[16] P. Ligarius, Observateurs de systemes bilinéaires a parametres répartis - Applications a un échangeur thermique, Thèse, Univ. de Rouen, Rouen, 1995.

[17] V. Lakshmikantham and S. Leela, Nonlinear differential equations in abstract spaces, Pergamon 1981. | MR 616449 | Zbl 0456.34002

[18] N. Tanaka and K. Kobayashi, Nonlinear semigroups and evolution equations governed by generalized dissipative operators, Adv. Math. Sci. Appl., Tokyo, Vol. 3, 1994, pp. 401-426. | Zbl 0818.34033

[19] W. Walter, Differential and integral inequalities, Springer-Verlag, 1970. | MR 271508 | Zbl 0252.35005

[20] C.Z. Xu, Exact observability and exponential stability of infinite dimensional bilinear systems, Math. Control Signal Systems, Vol. 9 (1), 1996, pp. 73-93 | MR 1410049 | Zbl 0862.93007