Le Thi Mai Thanh, Le Thi Phuong Ngoc, Nguyen Huu Nhan, Nguyen Thanh Long
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引用次数: 0
Abstract
In this paper, a class of fourth-order viscoelastic wave equations with damping terms is studied. First, the local existence and uniqueness of weak solutions for the proposed problem are proved by the linear approximation and the Faedo-Galerkin method. Next, a special case of the original problem is considered. Then, under some suitablely sufficient conditions on the relaxation functions and by using contrary arguments, we show that the corresponding problem in this case does not admit any global solutions. Ultimately, we prove the finite-time blow up of solutions in case of negative initial energy.
期刊介绍：
The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.
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