Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation

Applied Mathematics and Computation

Volumn 161, Issue 3, 2005, Pages 697-706

  Labidi, Soraya ^a   Tatar, Nasser Eddine ^b  

^a BADJI MOKHTAR UNIVERSITY   (Algeria)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Euler Bernoulli beam equation; Exponential growth; Fourier transforms; Fractional derivative; Hardy Littlewood Sobolev inequality

Indexed keywords

BOUNDARY CONDITIONS; DAMPING; DIFFERENTIATION (CALCULUS); FOURIER TRANSFORMS; PROBLEM SOLVING; SET THEORY; VISCOSITY;

EULER-BERNOULLI BEAM EQUATIONS; EXPONENTIAL GROWTH; FRACTIONAL DERIVATIVES; HARDY-LITTLEWOOD-SOBOLEV INEQUALITIES;

NONLINEAR EQUATIONS;

EID: 10644286405     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.12.057     Document Type: Article

References (11)

1. R. Gorenflo, Abel Integral Equations, Lecture Notes in Mathematics, vol. 1461, Springer-Verlag, Berlin, 1991.
2. G. Gripenberg, S.O. Londen, O. Staffans, Volterra integral and functional equations, Cambridge University Press, Cambridge, 1990.
3. L. Hörmander, The Analysis of Linear Partial Differential Operator, vol. I, Springer-Verlag, Berlin, 1983.
4. M. Kirane, N.-E. Tatar, Exponential growth for a fractionally damped wave equation, Zeit. Anal. Anw. 22 (1) (2003) 167-177.
5. M. Kirane, N.-E. Tatar, A memory type boundary stabilization of a mildly damped wave equation, Electr. J. Qual. Theory Diff. Eqs. 6 (1999) 1-7.
6. M. Kirane, N.-E. Tatar, Nonexistence results for a semilinear hyperbolic problem with boundary condition of memory type, Zeit. Anal. Angw. 19 (2) (2000) 1-16.
7. J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Grundlehren der Mathematishen Wissenschaften, vol. 181, Springer-Verlag, Berlin, New York, 1972.
8. G. Montseny, J. Audonnet, D. Matignon, Fractional integrodifferential boundary control of the Euler-Bernoulli beam, Publication du Département Traitement du Signal et de l'Image, Ecole Normale Superieur de Télécommunication, 98C003, October 1998.
9. K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
10. I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198, Academic Press, 1999.
11. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, Amsterdam, 1993 [Engl. Trans. from the Russian 1987].