具有退化阻尼项的粘弹性耦合波动方程解的局部存在性和爆破性

IF 0.7 Q4 MECHANICS

Theoretical and Applied Mechanics Pub Date : 2020-01-01 DOI:10.2298/tam200428008p

E. Pişkin, F. Ekinci, K. Zennir

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引用次数: 7

摘要

．本文研究了一类具有退化阻尼和源项的非线性粘弹性方程组。在适当的参数、退化阻尼项和松弛函数𝜛，(至极)，(至极= 1,2)的假设下，利用Faedo-Galerkin方法在新的情形下证明了解的局部存在性和唯一性。然后，我们证明了问题(1.1)的弱解的爆破性。这改进了先前文献中的结果[6,23,25]。

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Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms

. In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions 𝜛 𝑖 , ( 𝑖 = 1 , 2), we prove local existence and unique- ness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [ 6 , 23 , 25 ].

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来源期刊

Theoretical and Applied Mechanics MECHANICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

32 weeks

期刊介绍： Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.