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 bounded domain $R^{n}$. Under suitable conditions on variable exponents and initial data, prove that solutions will grow up as an exponential function with positive energy level. Our result improves extends many earlier results in literature such by Mahdi Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M).