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

Facta Universitatis. Series Mathematics and Informatics

article

Mohammad Shahrouzi¹ 

[1] Jahrom University

关键词: Variable exponents;    viscoelastic equation;    weak solution;   

DOI  :  10.22190/FUMI210222035S

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Nishu / University of Nis

【 摘 要 】

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).

【 授权许可】

Unknown