Well posedness and control of semilinear wave equations with iterated logarithms

Piermarco Cannarsa; Vilmos Komornik; Paola Loreti

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 37-56
  • ISSN: 1292-8119

How to cite

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Cannarsa, Piermarco, Komornik, Vilmos, and Loreti, Paola. "Well posedness and control of semilinear wave equations with iterated logarithms." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 37-56. <http://eudml.org/doc/90546>.

@article{Cannarsa1999,
author = {Cannarsa, Piermarco, Komornik, Vilmos, Loreti, Paola},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {global existence for all initial data; exact controllability; integral inequality},
language = {eng},
pages = {37-56},
publisher = {EDP Sciences},
title = {Well posedness and control of semilinear wave equations with iterated logarithms},
url = {http://eudml.org/doc/90546},
volume = {4},
year = {1999},
}

TY - JOUR
AU - Cannarsa, Piermarco
AU - Komornik, Vilmos
AU - Loreti, Paola
TI - Well posedness and control of semilinear wave equations with iterated logarithms
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 37
EP - 56
LA - eng
KW - global existence for all initial data; exact controllability; integral inequality
UR - http://eudml.org/doc/90546
ER -

References

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  1. [1] T. Cazenave and A. Haraux, Équations d'évolution avec non linéarité logarithmique. Ann. Fac. Sci. Toulouse 2 ( 1980) 21-51. Zbl0411.35051MR583902
  2. [2] T. Cazenave and A. Haraux, Introduction aux problèmes d'évolution semi-linéaires. Mathématiques et applications, Vol. 1, Ellipses et SMAI, Paris ( 1990). Zbl0786.35070MR1299976
  3. [3] P. Erdős, On the law of the iterated logarithm. Ann. of Math. 43 ( 1942) 419-436. Zbl0063.01264MR6630
  4. [4] O.Yu. Imanuvilov, Boundary control of semilinear evolution equations. Russian Math. Surveys 44 ( 1989183-184. Zbl0713.93030MR1024065
  5. [5] Li Ta-Tsien and Bing-Yu Zhang, Global exact controllability of a class of quasilinear hyperbolic systems. J. Math. Anal. Appl. 225 ( 1998289-311. Zbl0915.93007MR1639252
  6. [6] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier-Villars, Paris ( 1969). Zbl0189.40603MR259693
  7. [7] V.G. Maz'ja, Sobolev Spaces. Springer-Verlag, New York ( 1985). MR817985
  8. [8] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York ( 1983). Zbl0516.47023MR710486
  9. [9] S.L. Sobolev, Partial Differential Equations of Mathematical Physics. Dover, New York ( 1989). Zbl0123.06508
  10. [10] E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. Inst. H. Poincaré Anal. Non Linéaire 10 ( 1993) 109-129. Zbl0769.93017MR1212631

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