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Stability for the beam equation with memory in non‐cylindrical domains
Author(s) -
Ferreira J.,
Santos M. L.,
Matos M. P.
Publication year - 2004
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.507
Subject(s) - mathematics , infinity , constant (computer programming) , beam (structure) , boundary (topology) , mathematical analysis , stability (learning theory) , exponential decay , boundary value problem , exponential stability , physics , quantum mechanics , optics , nonlinear system , machine learning , computer science , programming language
In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the beam equation with memory and weak damping$$ {u_{tt}+\Delta^2u-\Delta u + \int_0^t g(t-s)\Delta u(s)ds+ \alpha u_t=0}\quad in\, {\hat{Q}}$$ where ${\hat{Q}}$ is a non‐cylindrical domains of ℝ n +1 ( n ⩾1) with the lateral boundary ${\hat{\sum}}$ and α is a positive constant. Copyright © 2004 John Wiley & Sons, Ltd.
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