Viscoelastic versus frictional dissipation in a variable coefficients plate system with time-varying delay
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In this paper, we are concerned with variable coefficients plate system subjected to three partially distributed feedbacks: time-varying delay, frictional and viscoelastic dissipations. This work is devoted to, without any prior quantification of both decay rate of relaxation function and growth rate of frictional dissipation near the origin, establish a general decay result which corresponds to a certainly stable ODE. Our result extends the decay result obtained for some kind of problems with finite history to problem with infinite history. Moreover, this paper allows a wider class of kernels of infinite history, and the usual exponential and polynomial decay rates are only special cases. The proof is based on the multiplier method and some techniques about convex functionals.
KeywordsFrictional damping Infinite history Partially distributed feedbacks Time-varying delay Variable coefficients
Mathematics Subject Classification35B37 35L55 74D05 93D15
The authors cordially thank the anonymous referees for the valuable comments and suggestions which lead to the improvement of this paper. This work was partially supported by NNSF of China (11871315, 61374089), Natural Science Foundation of Shanxi Province of China (201801D121003) and Graduate student education innovation project of Shanxi Province of China (2018BY025).
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