Well posedness and control of semilinear wave equations with iterated logarithms
Piermarco Cannarsa; Vilmos Komornik; Paola Loreti
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 4, page 37-56
- ISSN: 1292-8119
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topCannarsa, 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 (2010): 37-56. <http://eudml.org/doc/197290>.
@article{Cannarsa2010,
abstract = {
Motivated by a classical work of Erdős we give rather precise necessary and sufficient
growth conditions on the nonlinearity in a semilinear wave equation in order to have global
existence for all initial data. Then we improve some former exact controllability theorems
of Imanuvilov and Zuazua.
},
author = {Cannarsa, Piermarco, Komornik, Vilmos, Loreti, Paola},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Wave equation; semilinear equation; integral inequality; global existence for all initial data; exact controllability},
language = {eng},
month = {3},
pages = {37-56},
publisher = {EDP Sciences},
title = {Well posedness and control of semilinear wave equations with iterated logarithms},
url = {http://eudml.org/doc/197290},
volume = {4},
year = {2010},
}
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
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 37
EP - 56
AB -
Motivated by a classical work of Erdős we give rather precise necessary and sufficient
growth conditions on the nonlinearity in a semilinear wave equation in order to have global
existence for all initial data. Then we improve some former exact controllability theorems
of Imanuvilov and Zuazua.
LA - eng
KW - Wave equation; semilinear equation; integral inequality; global existence for all initial data; exact controllability
UR - http://eudml.org/doc/197290
ER -
References
top- T. Cazenave and A. Haraux, Équations d'évolution avec non linéarité logarithmique. Ann. Fac. Sci. Toulouse2 (1980) 21-51.
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- P. Erdos, On the law of the iterated logarithm. Ann. of Math.43 (1942) 419-436.
- O.Yu. Imanuvilov, Boundary control of semilinear evolution equations. Russian Math. Surveys44 (1989) 183-184.
- Li Ta-Tsien and Bing-Yu Zhang, Global exact controllability of a class of quasilinear hyperbolic systems. J. Math. Anal. Appl.225 (1998) 289-311.
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier-Villars, Paris (1969).
- V.G. Maz'ja, Sobolev Spaces. Springer-Verlag, New York (1985).
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983).
- S.L. Sobolev, Partial Differential Equations of Mathematical Physics. Dover, New York (1989).
- E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. Inst. H. Poincaré Anal. Non Linéaire10 (1993) 109-129.
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