一类具有非线性边界反馈的变指数四阶粘弹性方程解的指数增长

IF 0.5 Q3 MATHEMATICS

Facta Universitatis-Series Mathematics and Informatics Pub Date : 2022-09-20 DOI:10.22190/fumi210222035s

M. Shahrouzi

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引用次数: 2

摘要

本文研究了$R^{n}$有界域上形式为$$|u_{t}|^{\rho(x)}u_{tt}+\Delta[(a+b|\Delta u|^{m(x)-2})\Delta u]-\int_{0}^{t}g(t-s)\Delta^{2}u(s)ds=|u|^{p(x)-2}u,$$的变指数四阶粘弹性方程。在变指数和初始数据的适当条件下，我们证明了解将成长为具有正初始能级的指数函数。我们的结果改进并扩展了许多早期文献中的结果，如Mahdi和Hakem (Ser。数学。Inform. 2020, https://doi.org/10.22190/FUMI2003647M)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK

In this paper we study a variable-exponent fourth-order viscoelastic equation of the form$$|u_{t}|^{\rho(x)}u_{tt}+\Delta[(a+b|\Delta u|^{m(x)-2})\Delta u]-\int_{0}^{t}g(t-s)\Delta^{2}u(s)ds=|u|^{p(x)-2}u,$$in a bounded domain of $R^{n}$. Under suitable conditions on variable exponents and initial data, we prove that the solutions will grow up as an exponential function with positive initial energy level. Our result improves and extends many earlier results in the literature such as the on by Mahdi and Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M).

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Facta Universitatis-Series Mathematics and Informatics MATHEMATICS-

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