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Global solution and asymptotic behavior for the variable coefficient beam equation with nonlinear damping
Author(s) -
Yan Long,
Ji Shuguan
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3527
Subject(s) - uniqueness , mathematics , nonlinear system , mathematical analysis , beam (structure) , variable (mathematics) , position (finance) , energy method , boundary value problem , exponential stability , initial value problem , variable coefficient , exponential decay , physics , finance , quantum mechanics , nuclear physics , optics , economics
This paper is concerned with the initial‐boundary value problem for a variable coefficient beam equation with nonlinear damping. Such a model arises from the vertical deflections of a damped extensible elastic inhomogeneous beam whose density depends on time and position. By using the Faedo–Galerkin method and energy method, we obtain the existence and uniqueness of global strong solution. Furthermore, the exponential decay estimate for the total energy is also derived. Copyright © 2015 John Wiley & Sons, Ltd.