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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2016
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Banach tér |
| Online Access: | http://acta.bibl.u-szeged.hu/55450 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 1-24 |
| ISSN: | 1417-3875 |