Citation: |
[1] |
S. A. Ambartsumian, M. V. Belubekyan and M. M. Minasyan, On the problem of vibrations of nonlinear elastic electroconductive plates in transverse and longitudinal magnetic fields, International Journal of Nonlinear Mechanics, 19 (1983), 141-149. |
[2] |
P. Acquistapace and B. Terreni, Some existence and regularity results for abstract non-autonomous parabolic equations, Journal of Mathematical Analysis and Applications, 99 (1984), 9-64.doi: 10.1016/0022-247X(84)90234-8. |
[3] |
S. Angenent, Nonlinear analytic semiflows, Proc. Roy. Soc. Edinburgh Sect. A, 115 (1990), 91-107.doi: 10.1017/S0308210500024598. |
[4] |
G. Avalos and I. Lasiecka, Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation, SIAM Journal of Mathematical Analysis, 29 (1998), 155-182.doi: 10.1137/S0036141096300823. |
[5] |
G. Avalos and I. Lasiecka, Exponential stability of a thermoelastic system without dissipation, Rend. Istit. Mat. Univ. Trieste, Special Volume Dedicated to Memory of P. Grisvard, XXVIII (1997), 1-28. |
[6] |
G. Avalos and I. Lasiecka, On the null-controllability of thermoelastic plates and singularity of the associated minimal energy function, Journal of Mathematical Analysis and its Applications, 10 (2004), 34-61.doi: 10.1016/j.jmaa.2004.01.035. |
[7] |
G. Avalos and I. Lasiecka, Uniform decays in nonlinear thermoelasticity, in "Optimal Control, Theory, Methods and Applications," Kluwer, 15 (1998), 1-22. |
[8] |
A. Benabdallah and M. G. Naso, Nullcontrolability of thermoelastic plates, Abstract and Applied Analysis, 7 (2002), 585-599.doi: 10.1155/S108533750220408X. |
[9] |
G. Y. Bagdasaryan, "Vibrations and Stability of Magnetoelastic Systems," Yerevan, 1999. (in Russian). |
[10] |
C. Dafermos, On the existence and asymptotic stability of solutions to the equations of nonlinear thermoelasticity, Arch. Rat. Mechanics. Anal., 29 (1968), 241-271.doi: 10.1007/BF00276727. |
[11] |
C. Dafermos and L. Hsiao, Development of singularities in solutions of the equations of nonlinear thermoelasticity, Quart. Appl. Math., 44 (1986), 463-474. |
[12] |
G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, Journal of Functional Analysis, 58 (1984), 107-124.doi: 10.1016/0022-1236(84)90034-X. |
[13] |
K. Deimling, "Nonlinear Functional Analysis," Springer, New York, 1985. |
[14] |
R. Denk, M. Hieber and J. Prüss, $\mathcalR$-boundedness, Fourier Multipliers and Problems of elliptic and parabolic type, Memoirs of the AMS, (2003). |
[15] |
R. Denk and R. Racke, $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations, Electronic Journal of Differential Equations, (2006). |
[16] |
R. Denk, Y. Shibata and R. Racke, $L^p$ theory for the linear thermoelastic plate equations in bounded and exterior domains, Konstanzer Schriften in Mathematik und Informatik, 240, February, (2008). |
[17] |
M. Eller, I. Lasiecka and R. Triggiani, Simultaneous exact-approximate boundary controllability of thermo-elastic plates with variable thermal coefficients and moment control, Journal of Mathematical Analysis and its Applications, 251 (2000), 452-478.doi: 10.1006/jmaa.2000.7015. |
[18] |
M. Eller, I. Lasiecka and R. Triggiani, Unique continuation result for thermoelastic plates, Inverse and Ill-Posed Problems, 9 (2001), 109-148. |
[19] |
D. Hasanyan, N. Hovakimyan, A. J. Sasane and V. Stepanyan, Analysis of nonlinear thermoelastic plate equations, in "Proceedings of the 43rd IEEE Conference on Decision and Control," 2 (2004), 1514-1519.doi: 10.1109/CDC.2004.1430258. |
[20] |
S. Hansen and B. Zhang, Boundary control of a linear thermoelastic beam, Journal of Mathematical Analysis and its Applications, 210 (1997), 182-205.doi: 10.1006/jmaa.1997.5437. |
[21] |
S. Hansen, Exponential decay in a linear thermoelastic rod, J. Math. Anal. Appl., 187 (1992), 428-442.doi: 10.1016/0022-247X(92)90217-2. |
[22] |
A. A. Ilyushin, "Plasticity. Part One. Elasticity-Plastic Deformations," OGIZ, Moscow-Leningrad, 1948. (Russian). |
[23] |
S. Jiang and R. Racke, "Evolution Equations in Thermoelasticity," Chapman and Hall, Boca Raton, FL, 2000. |
[24] |
J. U. Kim, On the energy decay of a linear thermoelastic bar and plate, SIAM Journal of Mathematical Analysis, 23 (1992), 889-899.doi: 10.1137/0523047. |
[25] |
H. Koch and I.Lasiecka, Backward uniqueness in linear thermo-elasticity with variable coefficients, Functional Analysis and Evolution Equations, special volume dedicated to G. Lumer, Birkhauser, (2007). |
[26] |
M. Köhne, J. Prüss and M. Wilke, On quasilinear parabolic evolution equations in wheighted $L_p$-spaces, J. Evol. Equ., 10 (2010), 443-463.doi: 10.1007/s00028-010-0056-0. |
[27] |
J.Lagnese, The reachability problem for thermoelastic plates, Archive for Rational Mechanics and Analysis, 112 (1990), 223-267.doi: 10.1007/BF00381235. |
[28] |
J. Lagnese, "Boundary Stabilization of Thin Plates," SIAM, 1989.doi: 10.1137/1.9781611970821. |
[29] |
I. Lasiecka, Uniform decay rates for full von Karman system of dynamic thermoelasticity with free boundary conditions and partial boundary dissipation, Communications in Partial Differential Equations, 24 (1999), 1801-1847.doi: 10.1080/03605309908821483. |
[30] |
I. Lasiecka and C. Lebiedzik, Asymptotic behavior of nonlinear structural acoustic interactions with thermal effects on the interface, Nonlinear Analysis, 49 (2002), 703-735.doi: 10.1016/S0362-546X(01)00135-3. |
[31] |
I. Lasiecka and C. Lebiedzik, Boundary stabilizability of nonlinear structural acoustic models with thermal effects on the interface, C.R. Acad. Sci. Paris, 328 (2000), 187-192.doi: 10.1016/S1287-4620(00)00111-3. |
[32] |
I. Lasiecka, S. Maad and A. Sasane, Existence and exponential decay of solutions to a quasilinear thermoelastic plate system, NODEA, 15 (2008), 689-715.doi: 10.1007/s00030-008-0011-8. |
[33] |
I. Lasiecka and T. Seidman, Blowup estimates for observability of a thermoelastic system, Asymptotic Analysis, 50 (2006), 93-120. |
[34] |
I. Lasiecka and R. Triggiani, Structural decomposition of thermoelastic semigroups with rotational forces, Semigroup Forum, 60 (2000), 16-60.doi: 10.1007/s002330010003. |
[35] |
I. Lasiecka and R. Triggiani, "Control Theory for PDEs," Cambridge University Press, 1 (2000). |
[36] |
I. Lasiecka, M. Renardy and R. Triggiani, Backward uniqueness of thermoelastic plates with rotational forces, Semigroup Forum, 62 (2001), 217-242.doi: 10.1007/s002330010035. |
[37] |
I. Lasiecka and R. Triggiani, Exact null-controllability of structurally damped and thermoelastic parabolic models, Rend. Mat. Acta Lincei, 9 (1998), 43-69. |
[38] |
I. Lasiecka and R. Triggiani, Analyticity, and lack thereof, of thermoelastic semigroups, European Series in Applied and Industrial Mathematics, 4 (1998), 199-222.doi: 10.1051/proc:1998029. |
[39] |
L. Librescu, "Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-type Structures," Noordhoff, Leiden, 1975.doi: 10.1115/1.3423921. |
[40] |
L. Librescu, D. Hasanyan, Z. Qin and D. Ambur, Nonlinear magnetothermoelasticity of anisotropic plates in a magnetic field, Journal of Thermal Stresses, 26 (2003), 1277-1304.doi: 10.1080/714050886. |
[41] |
Z. Liu and M. Renardy, A note on the equation of a thermoelastic plate, Appl. Math. Letters, 8 (1995), 1-6.doi: 10.1016/0893-9659(95)00020-Q. |
[42] |
A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhauser, 1995.doi: 10.1007/978-3-0348-9234-6. |
[43] |
A. Lunardi, Abstract quasilinear parabolic equations, Math. Ann., 267 (1984), 395-415.doi: 10.1007/BF01456097. |
[44] |
A. Lunardi, Global solutions of abstract quasilinear parabolic equations, Journal Differential Equations, 58 (1985), 228-242.doi: 10.1016/0022-0396(85)90014-2. |
[45] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.doi: 10.1007/978-1-4612-5561-1. |
[46] |
J. Prüss, Maximal regularity for evolution equations in $L_p$-spaces, Conf. Semin. Mat. Univ. Bari, (2002), 1-39. |
[47] |
J. Prüss and G. Simonett, Maximal regularity for evolution equations in weighted $L_p$-spaces, Arch. Math., 82 (2004), 415-431.doi: 10.1007/s00013-004-0585-2. |
[48] |
J. E. Muñoz Rivera and R. Racke, Smoothing properties, decay, and global existence of solutions to nonlinear coupled systems of thermoelastic type, SIAM Journal on Mathematical Analysis, 26 (1995), 1547-1563.doi: 10.1137/S0036142993255058. |
[49] |
J. E. Muñoz Rivera and R. Racke, Large solutions and smoothing properties for nonlinear thermoelastic systems, Journal of Differential Equations, 127 (1996), 454-483.doi: 10.1006/jdeq.1996.0078. |
[50] |
H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators," North-Holland, 1978. |