带阻尼项的四阶粘弹性波动方程解的有限时间爆破

IF 1 4区数学 Q3 MATHEMATICS, APPLIED Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI:10.11948/20230162

Le Thi Mai Thanh, Le Thi Phuong Ngoc, Nguyen Huu Nhan, Nguyen Thanh Long

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引用次数: 0

摘要

研究了一类含阻尼项的四阶粘弹性波动方程。首先，利用线性逼近和Faedo-Galerkin方法证明了问题弱解的局部存在唯一性。接下来，考虑原问题的一种特殊情况。然后，在松弛函数的适当充分条件下，利用相反的论据，证明了在这种情况下对应的问题不存在全局解。最后，我们证明了初始能量为负时解的有限时间爆破。

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FINITE-TIME BLOW UP OF SOLUTIONS FOR A FOURTH-ORDER VISCOELASTIC WAVE EQUATION WITH DAMPING TERMS

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.

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来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

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.