Evolution equations governed by families of weighted operators

J. F. Couchouron; P. Ligarius

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 3, page 299-334
  • ISSN: 0294-1449

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Couchouron, J. F., and Ligarius, P.. "Evolution equations governed by families of weighted operators." Annales de l'I.H.P. Analyse non linéaire 16.3 (1999): 299-334. <http://eudml.org/doc/78467>.

@article{Couchouron1999,
author = {Couchouron, J. F., Ligarius, P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Cauchy problem; infinite-dimensional system; coherence; mild solution; weak* convergence},
language = {eng},
number = {3},
pages = {299-334},
publisher = {Gauthier-Villars},
title = {Evolution equations governed by families of weighted operators},
url = {http://eudml.org/doc/78467},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Couchouron, J. F.
AU - Ligarius, P.
TI - Evolution equations governed by families of weighted operators
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 3
SP - 299
EP - 334
LA - eng
KW - Cauchy problem; infinite-dimensional system; coherence; mild solution; weak* convergence
UR - http://eudml.org/doc/78467
ER -

References

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  1. [1] P. Bénilan, Équations d'évolution dans un espace de Banach quelconque et applications, Thèse, Paris-XI, Orsay, 1972. Zbl0246.47068
  2. [2] Ph. Bénilan, M.G. Crandall and A. Pazy, Evolution equations governed by accretive operators, Book (to appear). Zbl0895.47036
  3. [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. Zbl0485.93015MR661034
  4. [4] H. Brezis, Analyse fonctionnelle - Théorie et applications, Masson, Paris, 1992. Zbl0511.46001MR697382
  5. [5] J.-F. Couchouron, Équations d'évolution: Le problème de Cauchy, Univ. de Rouen, Rouen, These, 1993. 
  6. [6] J.-F. Couchouron, Problème de Cauchy non autonome pour des équations d'évolution, à paraitre. 
  7. [7] J.-F. Couchouron and P. Ligarius, Weighted evolution equations and asymptotic observers in Banach spaces. A nonlinear approach, submitted. 
  8. [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. Zbl0637.47039MR843569
  9. [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. Zbl0351.34037MR390853
  10. [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. Zbl0226.47038MR287357
  11. [11] J. Diestel and J. Uhl Jr., Vector measure, Math. surveys - AMS, Vol. 15, 1977. Zbl0369.46039MR453964
  12. [12] L.C. Evans, Nonlinear evolution equations in an arbitrary Banach space, Israël J. Math., Vol. 26 (1), 1977, pp. 1-42. Zbl0349.34043MR440431
  13. [13] Hartman, Ordinary Differential Equations, J. Wiley & Sons1964. Zbl0125.32102
  14. [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. Zbl0817.93055MR1297095
  15. [15] K. Kobayasi, Y. Kobayashi and S. Oharu, Nonlinear evolution operators in Banach spaces, Osaka J. Math., Vol. 21, 1984, pp. 281-310. Zbl0567.47047MR752464
  16. [16] P. Ligarius, Observateurs de systemes bilinéaires a parametres répartis — Applications a un échangeur thermique, Thèse, Univ. de Rouen, Rouen, 1995. 
  17. [17] V. Lakshmikantham and S. Leela, Nonlinear differential equations in abstract spaces, Pergamon1981. Zbl0456.34002MR616449
  18. [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. Zbl0818.34033
  19. [19] W. Walter, Differential and integral inequalities, Springer-Verlag, 1970. Zbl0252.35005MR271508
  20. [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 Zbl0862.93007MR1410049

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