MR2239913
Boris V. KAPITONOV and G. Perla MENZALA
Boris V. KAPITONOV and G. Perla MENZALA
Boundary Stabilization and a Problem of Transmission for a System of Propagation of Sound
Funkcialaj Ekvacioj. Serio Internacia
49
2006
107--132
http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-1/49_107.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2239913
We consider a transmission problem for a model describing the evolution of sound in a compressible fluid. Assuming that dissipative mechanisms of memory type are effective in part of the boundary, the coefficients are piecewise constants and suitable geometric conditions on the domain and the interfaces, we prove that the total energy associated with the model decays exponentially fast as $t\to+\infty$.
Boundary stabilization, Transmission problem, Multiplier method.
35Q99, 35S35, 35L99.
49-107
2006
Boundary Stabilization and a Problem of Transmission for a System of Propagation of Sound
KAPITONOV, Boris V. and MENZALA, G. Perla
Boris V. KAPITONOV and G. Perla MENZALA
1
Berti, V.
A dissipative boundary condition in electromagnetism: Existence, uniqueness and asymptotic stability
Riv. Mat. Univ. Parma (6)
1
1998
155-172
MR1685041
2
Fabrizio, M.; Morro, A.
A boundary condition with memory in electromagnetism
Arch. Rational Mech. Anal.
136
1996
359-381
MR1423012
3
Duvaut, G.; Lions, J.-L.
Les inéquations en Mécanique et en Physique
Dunod, Paris
1972
MR0464857
4
Kapitonov, B. V.
Uniform stabilization and simultaneous exact boundary controllability for a pair of hyperbolic systems
Siberian Math. J.
35
1994
722-734
MR1302434
5
Kapitonov, B. V.
Stabilization and exact boundary controllability for a Maxwell's equations
SIAM, J. Control Optim.
32
1994
408-421
MR1261146
6
Kapitonov, B. V.; Perla Menzala, G.
Uniform stabilization for Maxwell equations with boundary conditions with memory
Asymptot. Anal.
26
2001
91-104
MR1832580
7
Kapitonov, B. V.; Perla Menzala, G.
Energy decay and a transmission problem in electromagneto-elasticity
Adv. Differential Equations
7
2002
819-846
MR1895167
8
Kapitonov, B. V.; Raupp, M. A., Uniform stabilization for the system of evolution of sound in a compressible fluid with memory, Preprint No 38 (2002) at LNCC/MCT
9
Komornik, V.
Boundary stabilization, observation and control of Maxwell equations
Panamer. Math. J.
4
1994
47-61
MR1310321
10
Lagnese, J. E.
Boundary controllability in problems of transmission for a class of second order hyperbolic systems
ESAIM Control Optim. Calc. Var.
2
1997
343-357
MR1487483
11
Lasiecka, I.
Global uniform decay rates for the solutions to wave equation with nonlinear boundary conditions
Appl. Anal.
47
1992
191-212
MR1333954
12
Lasiecka, I.; Tataru, D.
Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
Differential Integral Equations
6
1993
507-533
MR1202555
13
Leis, R.
Initial boundary value problems in Mathematical Physics
John Wiley, New York
1986
MR0841971
14
Lions, J.-L.
Contrôlabilité exacte des systèmes distribués
C.R. Acad. Sci. Paris. Ser. I Math.
302
1986
471-475
MR0838402
15
Lions, J.-L.
Contrôlabilité exacte, perturbations et stabilisation des systèmes distribués, Tome 1, Contrôlabilité exacte
Coll. RMA, V. 8, Masson, Paris
1988
MR0953547
16
Martinez, P.
Boundary stabilization of the wave equation in almost star-shaped domains
SIAM, J. Control Optim.
37
1999
673-694
MR1675149
17
Nicaise, S.
Boundary exact controllability of interface problems with singularities, I: addition of the coefficients of singularities
SIAM, J. Control Optim.
34
1996
1512-1532
MR1404844
18
Nicaise, S.
Boundary exact controllability of interface problems with singularities, II: addition of internal control
SIAM, J., Control Optim.
35
1997
585-603
MR1436640
19
Pazy, A.
On the applicability of Lyapunov's theorem in Hilbert space
SIAM, J. Math. Anal.
3
1972
291-294
MR0317105
20
Propst, G.; Prüss, J.
On wave equations with boundary dissipation of memory type
J. Integral Equations Appl.
8
1996
99-123
MR1391147