Wellposedness and regularity of second order abstract equations arising in hyperbolic-like problems with nonlinear boundary conditions

Osaka Journal of Mathematics

Volumn 32, Issue 3, 1995, Pages 721-752

  Favini, Angelo ^a   Lasiecka, Irena ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF VIRGINIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972576260     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. R. Adams: Sobolev Spaces, Academic Press, New York, 1975.
2. A. Ambrosetti and G. Prodi: Analisi Non Lineare, Pisa, 1973.
3. V. Barbu: Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leyden, The Netherlands, 1976.
4. H. Brezis: Operateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North Holland, Mathematics Studies, Amsterdam, 1973.
5. V. Barbu and A. Favini: Existence for implicit differential equations in Banach spaces, Rend. Mat. Acc.Lincei, 3, (1992), 203-215.
6. M.E. Bradley and Lasiecka S: Local exponential stabilization of a nonlinearly perturbed von Karman plate, J. Nonlinear Anal. Theory, Methods and Appl. 18, No. 4, (1992), 333-343.
7. V.V. Bolotin: Nonconservative Problems of the Theory of Elastic Stability, Fizmatgiz, Moscow 1961. English Translation, Pergamon Press, Oxford and Macmillan, New York, 1963.
8. D. Chueshov: Strong solutions and the attractor of the von Karman equations, Math. USSR Sbornik 69 (1)(1991), 25-36.
9. R. D. Carroll and R.E. Showalter: Singular and Degenerate Cauchy Problems, Academic Press, New York, 1976.
10. W. Desch. I. Lasiecka and W. Shappacher: Feedback boundary control problems for linear semigroups, Israel J. Math. 51, No. 3(1985), 177-207.
11. W.F. Fitzgibbon: Strongly damped quasilinear evolution equations, J. Math.Anal. Appl. 42(1981), 536-550.
12. A. Favini, M.A. Horn, I. Lasiecka, D. Tataru. Global existence, uniqueness and regularity of solutions to the dynamic von Karman system with nonlinear boundary dissipation, to appear on Diff. Int. Eqs., 1995.
13. A. Favini, I. Lasiecka and H. Tanabe: Abstract differential equations and nonlinear dispersive systems, J. Diff. Integr. Eq. 6, No. 5 (1993), 995-1008.
14. P. Grisvard: Elliptic Problems in Nonsmooth Domains, Pitman, London, 1985.
15. T. Kato: Perturbation Theory for Linear Operators, Springer Verlag, 1966.
16. S. Kesavan: Topics in Functional Analysis and Applications, J. Wiley, 1987.
17. K. Koch and A. Stahel: Global existence of classical solutions to the dynamical von Karman equations, preprint.
18. J. Lagnese: Boundary Stabilization of Thin Plates, SIAM, Philadelphia, 1983.
19. J.L. Lions: Quelques Méthodes de Résolution des Problèmes aux Limit Nonlinéaires, Dunod, Paris, 1969.
20. J. Lagnese: Local controllability of dynamic von Karman plates, Control and Cybernetics 19 (1990), 155-168.
21. J.L. Lions: Contrôllabilite Exacte perturbations et stabilization des Systèmes Distribués, Masson, Paris, 1988.
22. H. Lasiecka: Stabilization of wave and plate equations with nonlinear dissipation on the boundary, J. Diff. Eq. 78 2 (1983), 340-381.
23. H. Lagnese and G. Leugering: Uniform stabilization of a nonlinear beam by nonlinear feedback, J.D.Eq. 91 (1981), 355-388.
24. V. Lakshmikantham and S. Leela: Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford, 1981.
25. J.L. Lions and E. Magenes: Non Homogeneous Boundary Value Problems and Applications, Vol. 1, Springer-Verlag, New York, 1972.
26. I. Lasiecka and R. Triggiani: Lifting theorem for the time regularity of solutions to abstract equations, Proc. Amer. Math. Soc 104, No. 3, (1988), 745-755.
27. I. Lasiecka and R. Triggiani: Trace regularity of the solutions of the wave equation with homogeneous Neumann boundary conditions and data supported away from the boundary, J. Math. Anal. Appl. 141, No. 1 (1989), 49-71.
28. I. Lasiecka and R. Triggiani: Differential and Algebraic Riccati Equations with Applications to Boundary Point Control Problems: Continuous Theory and Approximation Theory, Vol. 164, Springer Verlag, LNCIS, 1991.
29. A.H. Nayfeh and D.T. Mook: Nonlinear Oscillations, Wiley-Interscience, 1979.
30. A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
31. E. Reiss and B. Matkowski: Nonlinear dynamic buckling of a compressed elastic column, Quart. Appl. Math. 29 (1971), 245-260.
32. R.E. Showalter: Hilbert Space Methods for Partial Differential Equations, Pitman, London, 1977.
33. A. Stahel: A remark on the equation of a vibrating plate. Proc. Royal Soc. Edinburgh 136A (1987), 307-314.
34. H. Tanabe: Equation of Evolution, Pitman London, 1979.
35. W. von Wahl: On nonlinear evolution equations in a Banach space and on nonlinear vibrations of the clamped plate, Bayreuther Math. Schrif. 20 (1985), 205-209.
36. M. Wojnowski and A. Krieger: The effect of axial force on the vibrations of hinged bars, J. Appl.Mech. 17 (1950), 35-36.