-
1
-
-
0003796630
-
-
Academic Press, New York
-
R. A. ADAMS, Sobolev Spaces, Academic Press, New York, 1975.
-
(1975)
Sobolev Spaces
-
-
ADAMS, R.A.1
-
2
-
-
0026923885
-
Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary
-
C. BARDOS. G. LEBEAU, AND J. RAUCH, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), pp. 1024-1065.
-
(1992)
SIAM J. Control Optim
, vol.30
, pp. 1024-1065
-
-
BARDOS, C.1
LEBEAU, G.2
RAUCH, J.3
-
3
-
-
0036014250
-
One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms
-
P. CANNARSA, V. KOMORNIK, AND P. LORETI, One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms, Discrete Contin. Dyn. Syst. B, 8 (2002), pp. 745-756.
-
(2002)
Discrete Contin. Dyn. Syst. B
, vol.8
, pp. 745-756
-
-
CANNARSA, P.1
KOMORNIK, V.2
LORETI, P.3
-
4
-
-
0002528717
-
Equations d'évolution avec non-linéarité logarithmique
-
T. CAZENAVE AND A. HARAUX, Equations d'évolution avec non-linéarité logarithmique, Ann. Fac. Sci. Toulouse, 2 (1980), pp. 21-51.
-
(1980)
Ann. Fac. Sci. Toulouse
, vol.2
, pp. 21-51
-
-
CAZENAVE, T.1
HARAUX, A.2
-
5
-
-
0016891177
-
Controllability of the nonlinear wave equation in several space variables
-
W. C. CHEWNING, Controllability of the nonlinear wave equation in several space variables, SIAM J. Control Optim., 14 (1976), pp. 19-25.
-
(1976)
SIAM J. Control Optim
, vol.14
, pp. 19-25
-
-
CHEWNING, W.C.1
-
6
-
-
0014509719
-
Boundary controllability of nonlinear hyperbolic systems
-
M. CIRINÁ, Boundary controllability of nonlinear hyperbolic systems, SIAM J. Control, 7 (1969), pp. 198-212.
-
(1969)
SIAM J. Control
, vol.7
, pp. 198-212
-
-
CIRINÁ, M.1
-
7
-
-
31844433671
-
Rotated weights in global Carleman estimates applied to an inverse problem for the wave equation
-
A. DOUBOVA AND A. OSSES, Rotated weights in global Carleman estimates applied to an inverse problem for the wave equation, Inverse Problems, 33 (2006), pp. 265-296.
-
(2006)
Inverse Problems
, vol.33
, pp. 265-296
-
-
DOUBOVA, A.1
OSSES, A.2
-
8
-
-
52649134300
-
On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials
-
to appear
-
T. DUYCKAERTS, X. ZHANG, AND E. ZUAZUA, On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.
-
Ann. Inst. H. Poincaré Anal. Non Linéaire
-
-
DUYCKAERTS, T.1
ZHANG, X.2
ZUAZUA, E.3
-
9
-
-
84956102700
-
Boundary controllability of semilinear evolution equations
-
O. YU. ÉMANUILOV, Boundary controllability of semilinear evolution equations, Russian Math. Surveys, 44 (1989), pp. 183-184.
-
(1989)
Russian Math. Surveys
, vol.44
, pp. 183-184
-
-
YU, O.1
ÉMANUILOV2
-
10
-
-
0001135182
-
Local controllability of a nonlinear wave equation
-
H. O. FATTORINI, Local controllability of a nonlinear wave equation, Math. Systems Theory, 9 (1975), pp. 30-45.
-
(1975)
Math. Systems Theory
, vol.9
, pp. 30-45
-
-
FATTORINI, H.O.1
-
11
-
-
0001433193
-
The cost of approximate controllability for heat equations: The linear case
-
E. FERNÁNDEZ-CARA AND E. ZUAZUA, The cost of approximate controllability for heat equations: The linear case, Adv. Differential Equations, 5 (2000), pp. 465-514.
-
(2000)
Adv. Differential Equations
, vol.5
, pp. 465-514
-
-
FERNÁNDEZ-CARA, E.1
ZUAZUA, E.2
-
12
-
-
33645293424
-
A weighted identity for partial differential operators of second order and its applications
-
X. FU, A weighted identity for partial differential operators of second order and its applications, C. R. Math. Acad. Sci. Paris, 342 (2006), pp. 579-584.
-
(2006)
C. R. Math. Acad. Sci. Paris
, vol.342
, pp. 579-584
-
-
FU, X.1
-
13
-
-
52649115223
-
Exact Controllability of the Heat Equation with Hyperbolic Memory Kernel in Anisotropic and Non-Homogeneous Media
-
preprint
-
X. FU, J. YONG, AND X. ZHANG, Exact Controllability of the Heat Equation with Hyperbolic Memory Kernel in Anisotropic and Non-Homogeneous Media, preprint, 2005.
-
(2005)
-
-
FU, X.1
YONG, J.2
ZHANG, X.3
-
14
-
-
52649175850
-
-
A. V. FURSIKOV AND O. YU. IMANUVILOV, Controllability of Evolution Equations, Lecture Notes Series 34, Research Institute of Mathematics, Seoul National University, Seoul, Korea, 1994.
-
A. V. FURSIKOV AND O. YU. IMANUVILOV, Controllability of Evolution Equations, Lecture Notes Series 34, Research Institute of Mathematics, Seoul National University, Seoul, Korea, 1994.
-
-
-
-
15
-
-
0000522384
-
On the Nash-Moser implicit function theorem
-
L. HÖRMANDER, On the Nash-Moser implicit function theorem, Ann. Acad. Sci. Fenn. Ser. A I Math., 10 (1985), pp. 255-259.
-
(1985)
Ann. Acad. Sci. Fenn. Ser. A I Math
, vol.10
, pp. 255-259
-
-
HÖRMANDER, L.1
-
18
-
-
0036975369
-
On Carleman estimates for hyperbolic equations
-
O. YU. IMANUVILOV, On Carleman estimates for hyperbolic equations, Asymptot. Anal., 32 (2002), pp. 185-220.
-
(2002)
Asymptot. Anal
, vol.32
, pp. 185-220
-
-
YU, O.1
IMANUVILOV2
-
19
-
-
52649116243
-
-
V. ISAKOV AND M. YAMAMOTO, Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse problems, in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemp. Math. 268, AMS, Providence, RI, 2000, pp. 191-225.
-
V. ISAKOV AND M. YAMAMOTO, Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse problems, in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemp. Math. 268, AMS, Providence, RI, 2000, pp. 191-225.
-
-
-
-
20
-
-
0002267569
-
Stability estimates for ill-posed Cauchy problem involving hyperbolic equations and inequalities
-
M. KAZEMI AND M. V. KLIBANOV, Stability estimates for ill-posed Cauchy problem involving hyperbolic equations and inequalities, Appl. Anal., 50 (1993), pp. 93-102.
-
(1993)
Appl. Anal
, vol.50
, pp. 93-102
-
-
KAZEMI, M.1
KLIBANOV, M.V.2
-
21
-
-
0347940923
-
Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data
-
M. V. KLIBANOV AND J. MALINSKY, Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data, Inverse Problems, 7 (1991), pp. 577-595.
-
(1991)
Inverse Problems
, vol.7
, pp. 577-595
-
-
KLIBANOV, M.V.1
MALINSKY, J.2
-
23
-
-
0002621804
-
Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems
-
I. LASIECKA AND R. TRIGGIANI, Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems, Appl. Math. Optim., 23 (1991), pp. 109-154.
-
(1991)
Appl. Math. Optim
, vol.23
, pp. 109-154
-
-
LASIECKA, I.1
TRIGGIANI, R.2
-
24
-
-
52649166696
-
-
I. LASIECKA, R. TRIGGIANI, AND X. ZHANG, Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot, in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemp. Math. 268, AMS, Providence, RI, 2000, pp. 227-325.
-
I. LASIECKA, R. TRIGGIANI, AND X. ZHANG, Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot, in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemp. Math. 268, AMS, Providence, RI, 2000, pp. 227-325.
-
-
-
-
25
-
-
52649179295
-
-
M. M. LAVRENT'EV, V. G. ROMANOV, AND S. P. SHISHATSKII, Ill-posed problems of mathematical physics and analysis, translated from the Russian by J. R. Schulenberger, Transl. Math. Monogr. 64, AMS, Providence, RI, 1986.
-
M. M. LAVRENT'EV, V. G. ROMANOV, AND S. P. SHISHATSKII, Ill-posed problems of mathematical physics and analysis, translated from the Russian by J. R. Schulenberger, Transl. Math. Monogr. 64, AMS, Providence, RI, 1986.
-
-
-
-
26
-
-
0034666915
-
Exact controllability for semilinear wave equations
-
L. LI AND X. ZHANG, Exact controllability for semilinear wave equations, J. Math. Anal. Appl., 250 (2000), pp. 589-597.
-
(2000)
J. Math. Anal. Appl
, vol.250
, pp. 589-597
-
-
LI, L.1
ZHANG, X.2
-
27
-
-
0141580730
-
Exact boundary controllability for quasi-linear hyperbolic systems
-
T.-T. LI AND B.-P. RAO, Exact boundary controllability for quasi-linear hyperbolic systems, SIAM J. Control Optim., 41 (2003), pp. 1748-1755.
-
(2003)
SIAM J. Control Optim
, vol.41
, pp. 1748-1755
-
-
LI, T.-T.1
RAO, B.-P.2
-
28
-
-
0003509253
-
-
Appl, Birkhäuser Boston, Inc, Boston, MA
-
X. LI AND J. YONG, Optimal Control Theory for Infinite-Dimensional Systems, Systems Control Found. Appl., Birkhäuser Boston, Inc., Boston, MA, 1995.
-
(1995)
Optimal Control Theory for Infinite-Dimensional Systems, Systems Control Found
-
-
LI, X.1
YONG, J.2
-
29
-
-
0003967917
-
-
Rech. Math. Appl. 8, Masson, Paris
-
J.-L. LIONS, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Contrôlabilité exacte, Rech. Math. Appl. 8, Masson, Paris, 1988.
-
(1988)
Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Contrôlabilité exacte
-
-
LIONS, J.-L.1
-
30
-
-
0038401228
-
Exact controllability in "arbitrarily short time" of the semilinear wave equation
-
P. MARTINEZ AND J. VANCOSTENOBLE, Exact controllability in "arbitrarily short time" of the semilinear wave equation, Discrete Contin. Dyn. Syst. B, 9 (2003), pp. 901-924.
-
(2003)
Discrete Contin. Dyn. Syst. B
, vol.9
, pp. 901-924
-
-
MARTINEZ, P.1
VANCOSTENOBLE, J.2
-
32
-
-
16244362048
-
Polynomial decay of a hyperbolic-parabolic coupled system
-
J. RAUCH, X. ZHANG, AND E. ZUAZUA, Polynomial decay of a hyperbolic-parabolic coupled system, J. Math. Pures Appl., 84 (2005), pp. 407-470.
-
(2005)
J. Math. Pures Appl
, vol.84
, pp. 407-470
-
-
RAUCH, J.1
ZHANG, X.2
ZUAZUA, E.3
-
33
-
-
0000820706
-
Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions
-
D. L. RUSSELL, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), pp. 639-739.
-
(1978)
SIAM Rev
, vol.20
, pp. 639-739
-
-
RUSSELL, D.L.1
-
34
-
-
17044453856
-
Invariance of the reachable set under nonlinear perturbations
-
T. I. SEIDMAN, Invariance of the reachable set under nonlinear perturbations, SIAM J. Control Optim., 25 (1987), pp. 1173-1191.
-
(1987)
SIAM J. Control Optim
, vol.25
, pp. 1173-1191
-
-
SEIDMAN, T.I.1
-
35
-
-
0001692117
-
Carleman estimates and unique continuation for solutions to boundary value problems
-
D. TATARU, Carleman estimates and unique continuation for solutions to boundary value problems, J. Math. Pures Appl., 75 (1996), pp. 367-408.
-
(1996)
J. Math. Pures Appl
, vol.75
, pp. 367-408
-
-
TATARU, D.1
-
36
-
-
0000105636
-
Explicit observability estimate for the wave equation with potential and its application
-
X. ZHANG, Explicit observability estimate for the wave equation with potential and its application, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 456 (2000), pp. 1101-1115.
-
(2000)
R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci
, vol.456
, pp. 1101-1115
-
-
ZHANG, X.1
-
37
-
-
0034437583
-
Explicit observability inequalities for the wave equation with lower order terms by means of Carleman inequalities
-
X. ZHANG, Explicit observability inequalities for the wave equation with lower order terms by means of Carleman inequalities, SIAM J. Control Optim., 39 (2000), pp. 812-834.
-
(2000)
SIAM J. Control Optim
, vol.39
, pp. 812-834
-
-
ZHANG, X.1
-
38
-
-
0035422081
-
Exact controllability of the semilinear plate equations
-
X. ZHANG, Exact controllability of the semilinear plate equations, Asymptot. Anal., 27 (2001), pp. 95-125.
-
(2001)
Asymptot. Anal
, vol.27
, pp. 95-125
-
-
ZHANG, X.1
-
40
-
-
0037294750
-
Decay of solutions of the system of thermoelasticity of type III
-
X. ZHANG AND E. ZUAZUA, Decay of solutions of the system of thermoelasticity of type III. Commun. Contemp. Math., 5 (2003), pp. 25-83.
-
(2003)
Commun. Contemp. Math
, vol.5
, pp. 25-83
-
-
ZHANG, X.1
ZUAZUA, E.2
-
41
-
-
4344698661
-
Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system
-
X. ZHANG AND E. ZUAZUA, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system, J. Differential Equations, 204 (2004), pp. 380-438.
-
(2004)
J. Differential Equations
, vol.204
, pp. 380-438
-
-
ZHANG, X.1
ZUAZUA, E.2
-
42
-
-
84884841555
-
Exact controllability of the semi-linear wave equation
-
V. D. Blondel and A. Megretski, eds, Princeton University Press, Princeton, NJ
-
X. ZHANG AND E. ZUAZUA, Exact controllability of the semi-linear wave equation, in Sixty Open Problems in the Mathematics of Systems and Control, V. D. Blondel and A. Megretski, eds., Princeton University Press, Princeton, NJ, 2004, pp. 173-178.
-
(2004)
Sixty Open Problems in the Mathematics of Systems and Control
, pp. 173-178
-
-
ZHANG, X.1
ZUAZUA, E.2
-
43
-
-
0003138438
-
Exact controllability for the semilinear wave equation
-
E. ZUAZUA, Exact controllability for the semilinear wave equation, J. Math. Pures Appl., 69 (1990), pp. 1-31.
-
(1990)
J. Math. Pures Appl
, vol.69
, pp. 1-31
-
-
ZUAZUA, E.1
-
44
-
-
52649105325
-
-
E. ZUAZUA, Exact boundary controllability for the semilinear wave equation, in Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, X (Paris, 1987-1988), Pitman Res. Notes Math. Ser. 220, Longman Sci. Tech., Harlow, 1991, pp. 357-391.
-
E. ZUAZUA, Exact boundary controllability for the semilinear wave equation, in Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. X (Paris, 1987-1988), Pitman Res. Notes Math. Ser. 220, Longman Sci. Tech., Harlow, 1991, pp. 357-391.
-
-
-
-
45
-
-
85012981810
-
Exact controllability for semilinear wave equations in one space dimension
-
E. ZUAZUA, Exact controllability for semilinear wave equations in one space dimension, Ann. Inst. H. Poincaré Anal. Non Linéaire, 10 (1993), pp. 109-129.
-
(1993)
Ann. Inst. H. Poincaré Anal. Non Linéaire
, vol.10
, pp. 109-129
-
-
ZUAZUA, E.1
|