On a beam equation in Banach spaces

This paper is concerned with the existence and asymptotic behavior of solutions of the Cauchy problem for an abstract model for vertical vibrations of a viscous beam in Banach spaces. First is obtained a local solution of the problem by using the method of successive approximations, a characterizati...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2016-01, Vol.2016 (110), p.1-24
Main Authors: Milla Miranda, Manuel, Ferreira Silva, Valdenilza, Rodrigues Carvalho, Ricardo
Format: Article
Language:English
Subjects:
asymptotic behavior
beam equation
global solution
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Summary:This paper is concerned with the existence and asymptotic behavior of solutions of the Cauchy problem for an abstract model for vertical vibrations of a viscous beam in Banach spaces. First is obtained a local solution of the problem by using the method of successive approximations, a characterization of the derivative of the nonlinear term of the equation defined in a Banach space and the Ascoli-Arzelà theorem. Then the global solution is found by the method of prolongation of solutions. The exponential decay of solutions is derived by considering a Lyapunov functional.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2016.1.110