Interlude of operator pairs and a von Kármán plate-beam problem with rotational inertia

Applicable Analysis

Volumn 75, Issue 3-4, 2000, Pages 349-369

  Grobbelaar Van Dalsen, Marié ^a  

^a UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

35Q72; 73D35; Coupled; Dynamic boundary condition; Empathy; Fractional powers; Interactive; Plate beam; Rotational inertia; Von K rm system

Indexed keywords

EID: 0008119007     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036810008840854     Document Type: Article

References (32)

1. Avalos, G., 1996. The exponential Stability of a coupled hyperbolic/ Parabolic System arising in structural Acoustics. Abstract and applied Analysis, 1: 203–219.
2. Bolotin, V.V., 1963. “ Nonconservative Problems of the Theory of elastic Stability ”. Oxford: Pergamon Press.
3. Bradley, M.E., 1992. Local exponential Stabilization of a nonlinearly perturbed von Kármán Plate. J.Nonlinear Anal.Theory Methods and Appl., 18: 33–343.
4. Bradley, M.E., and Lasiecka, I., 1993. Global Stabilization of a von Kármán Plate without geometric Conditions In: Identification and Control in Systems governed by Partial Differential Equations. SIAM,: 101–116.
5. Brenner, P., and Von Wahl, W., 1981. Global Solutions of nonlinear Wave Equations. Math. Z, 176: 87–121.
6. Chen, G., 1993. “ Vibration and damping in distributed Systems ”. London: CRC Press.
7. Chueshov, I.D., 1991. Storng Solutions and the Attractor of the von Kármán equations. USSR Sbornik, 69: 25–36.
8. Dautray, R., 1992. Mathematical Analysis and Numerical Methods for Science and Technology. 1.
9. Favini, A., Horn, M.A., and Tataru, D., 1996. Global Existence Uniqueness and Regularity of Solutions to a Von Kármá System with nonlinear Boundary Dissipation. Differential and Integral Equations, 9: 267–294.
10. Favini, A., and Lasiecka, I., 1995. Wellposedness and Regularity of second Order abstract Equations arising in Hyperbolic-like Problems with nonlinear Boundary Conditions. Osaka J.Math, 32: 721–752.
11. Fichera, G., 1983. On a class of Evolution problems. Proc. Royal Soc., 95: 247–256.
12. Grobbelaar and Van Dalsen, M., 149. Fractional Powers of a closed Pair of operators. Proc. Roy. Soc, 102: 158
13. Globbelaar and Van Dalsen, M., 1987. Semilinear Evolution Equations and Fractional Powers of a closed pair of Operator. Proc. Roy. Soc, 105: 101–115.
14. Grobbelaar, Van Dalsen, M., and Sauer, N., 1993. Solutions In Lebesgue spaces of the Navier-Stokes Equations with dynamic Boundary conditions. Proc. Roy. Soc, 123A: 745–761.
15. Grobbelaar and Van Dalsen, M., 1993. On Fractional Powers of a closed Pair of Operators and a damped Wave Equation with dynamic Boundary conditions. Applicable Analysis, 124: 221–237.
16. Grobbelaar and Van Dalsen, M., 1996. On the Solvability of the Boundaryvalue Problem for the elastic Beam with attached Load. Mathematical Models and Methods in Applied Sciences, 4 (1): 89–105.
17. Grobbelaar and Van Dalsen, M., 1996. On the Initial-value Problem for the extensible Beam with attached Load. Mathematical Methods in the Applied Sciences, 19: 943–957.
18. Grobbelaar and Van Dalsen, M., 1999. On fractional powers of a Pair of Matrices and a Platbeam. Appl. Anal, 72 (3–4): 369–390.
19. Lagnese, J.E., 1989. Boundary Stabilization of thin Plates SIAM.
20. Lagnese, J.E., 1990. Local Controllability of dynamic von Kármán Plates. Control an Cybernetics,: 155–168.
21. Lagnese, J.E., and Leugering, G., 1991. Uniform Stabilization of a nonlinear Beam by linear Feedback. J. Differential Equations, 91: 355–388.
22. Lagmese, J.E., Leugering, G., and Schmidt, E.J.P.G., 1994. Modeling, Analysis and Control of dynamic elastic Multi-Link Structures, Bostan: Birkhauser.
23. Lagmese, J.E., 1995. Modelling and Controllability of Plate-beam Systems. J.Math. Systems, Estim Control, 5: 141–187.
24. Lasiecka, I., 1996. Control and Stabilization of interactive Systems: In: Systems and control in the twenty-first Century. St. Louis, MO,: 245–262.
25. Lions, J.L., 1969. Quelques Methodes de Resolution des Problemes aux Limit nonlinearies.
26. Pazy, A., 1983. Semigroups of Linear Opertoars and Applications to Partial Differntial Equations.
27. Sauer, N., 1997. “ Empathy theory and the Laplace Transform ”. Vol. 38, 325–338. Linear Operators Banach Center Publications.
28. Stahel, A., 1987. A Remark on the equation of a vibrating Plate. Proc. Roy. Soc., 136 A: 307–314.
29. Tanabe, H., 1979. Equations of Evolution.
30. Van Der Merwe, A.J., 1988. B-evolutions and Sobolev equations. Appl. Anal, 29: 91–105.
31. Von Wahl, W., 1981. On Nonlinear Evolution equations in a Banach Space and on nonlinear Vibrations of a clamped Plate. Bayreuther Mathematische Schriften, 7: 1–93.
32. Von Wahl, W., 1985. On Nonlinear Evolution Equations in a Banach Space and on nonlinear vibrations of a clamper Plate. Bayreuther Mathematische Schriften, 20: 205–209.