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Well-posedness and exponential stability for a plate equation with time-varying delay and past history

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Abstract

This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback

$$\begin{aligned} u_{tt}+\alpha \Delta ^2 u-\int \limits ^t_{-\infty }g(t-s)\Delta ^2 u(s)\mathrm{d}s+\mu _1u_t+\mu _2u_t(t-\tau (t))+f(u)=h(x), \end{aligned}$$

defined in a bounded domain of \({\mathbb {R}}^n\) \((n\ge 1)\) with some suitable initial data and boundary conditions. For arbitrary real numbers \(\mu _1\) and \(\mu _2\), we proved the global well-posedness of the problem. Results on stability of energy are also proved under some restrictions on \(\mu _1\), \(\mu _2\) and \(h(x)=0\).

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Authors and Affiliations

  1. Faculty of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Baowei Feng

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Feng, B. Well-posedness and exponential stability for a plate equation with time-varying delay and past history. Z. Angew. Math. Phys. 68, 6 (2017). https://doi.org/10.1007/s00033-016-0753-9

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  • DOI: https://doi.org/10.1007/s00033-016-0753-9

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