On behaviour of solutions for a nonlinear viscoelastic equation with variable-exponent nonlinearities

Shahrouzi, Mohammad

doi:10.1016/j.camwa.2018.03.005

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Introduction4

Case Of Variable Exponents1

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Cited by 17 publications

(6 citation statements)

References 26 publications

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“…Shahrouzi [26] studied the behavior of solutions to the following initial-boundary value problem with variable-exponent nonlinearities…”

Section: Case Of Variable Exponentsmentioning

confidence: 99%

Exponential Growth of Solutions for a Variable-Exponent Fourth-Order Viscoelastic Equation With Nonlinear Boundary Feedback

Shahrouzi

2022

FU Math Inform

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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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“…Shahrouzi [26] studied the behavior of solutions to the following initial-boundary value problem with variable-exponent nonlinearities…”

Section: Case Of Variable Exponentsmentioning

confidence: 99%

Exponential Growth of Solutions for a Variable-Exponent Fourth-Order Viscoelastic Equation With Nonlinear Boundary Feedback

Shahrouzi

2022

FU Math Inform

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“…in a non-cylindrical domain. Recently, some other authors investigate hyperbolic type equations (see [11,[21][22][23][24][25]28]). Our aim in this work is to prove the stability of solutions for the Kirchhoff beam equation with the delay term (µ 2 u t (x,t − τ)) and variable exponents which make the problem more different than from those considered in the literature.…”

Section: Introductionmentioning

confidence: 99%

Stability Result for a Kirchhoff Beam Equation with Variable Exponent and Time Delay

Ferreira¹,

Pışkın

Raposo

et al. 2022

Universal Journal of Mathematics and Applications

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“…In recent years, some other authors investigate hyperbolic type equation with variable exponents (see [8,13,16,18,24]).…”

Section: Introductionmentioning

confidence: 99%

Nonexistence of global solutions of a delayed wave equation with variable-exponents

Pışkın¹,

Yüksekkaya²

2021

MMN

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On behaviour of solutions for a nonlinear viscoelastic equation with variable-exponent nonlinearities

Cited by 17 publications

References 26 publications

Exponential Growth of Solutions for a Variable-Exponent Fourth-Order Viscoelastic Equation With Nonlinear Boundary Feedback

Exponential Growth of Solutions for a Variable-Exponent Fourth-Order Viscoelastic Equation With Nonlinear Boundary Feedback

Stability Result for a Kirchhoff Beam Equation with Variable Exponent and Time Delay

Nonexistence of global solutions of a delayed wave equation with variable-exponents

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