Well posedness and control of semilinear wave equations with iterated logarithms

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 4, Issue , 1999, Pages 37-56

  Cannarsal, Piermarco ^a   Komornik, Vilmos ^b   Loreti, Paola ^c,d  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITÉ DE STRASBOURG   (France)

^c CNR   (Italy)

^d SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Integral inequality; Semilinear equation; Wave equation

Indexed keywords

BOUNDARY CONDITIONS; CONTROL NONLINEARITIES; CONTROLLABILITY; GLOBAL OPTIMIZATION; INITIAL VALUE PROBLEMS; ITERATIVE METHODS; MATHEMATICAL MODELS;

IMANUVILOV CONTROLLABILITY THEOREM; ITERATED LOGARITHMS; SEMILINEAR WAVE EQUATIONS; ZUAZUA CONTROLLABILITY THEOREM;

WAVE EQUATIONS;

EID: 0033276586     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:1999102     Document Type: Article

References (10)

1. T. Cazenave and A. Haraux, Equations d’évolution avec non linéarité logarithmique. Ann. Fac. Sci. Toulouse 2 (1980) 21-51.
2. T. Cazenave and A. Haraux, Introduction aux problèmes d'évolution semi-linéaires. Mathematiques et applications, Vol. 1, Ellipses et SMAI, Paris (1990).
3. P. Erdos, On the law of the iterated logarithm. Ann. of Math. 43 (1942) 419-436.
4. O.Yu. Imanuvilov, Boundary control of semilinear evolution equations. Russian Math. Surveys 44 (1989) 183-184.
5. 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.
6. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod—Gauthier-Villars, Paris (1969).
7. V.G. Maz’ja, Sobolev Spaces. Springer-Verlag, New York (1985).
8. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983).
9. S.L. Sobolev, Partial Differential Equations of Mathematical Physics. Dover, New York (1989).
10. E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993) 109-129.