Global Nonexistence of Solutions for a Class of Viscoelastic Lamé System

Shahrouzi, Mohammad

doi:10.1007/s13226-020-0472-y

Cited by 8 publications

(4 citation statements)

References 21 publications

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“…Due to the great importance both theoretically and practically, numerous researchers have studied equations with nonstandard growth conditions, that is, equations with the variable exponent of nonlinearities, [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Compared with equations with variable exponent nonlinearities, less work has been done in a system of equations with variable exponent nonlinearities.…”

Section: Variable Exponentsmentioning

confidence: 99%

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

Shahrouzi,

Ferreira,

Tahamtani

2023

Math Methods in App Sciences

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This work studies the global behavior of solutions for a system of ‐Kirchhoff‐type equations. We prove the global existence of solutions, and next, by constructing suitable auxiliary functionals, the general decay of solutions has been confirmed when the exponents satisfy appropriate conditions. Also, under suitable conditions on data, we establish the finite time blow‐up of solutions with negative initial energy. Our results extend and improve many earlier results in the literature.

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Section: Variable Exponentsmentioning

confidence: 99%

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

Shahrouzi,

Ferreira,

Tahamtani

2023

Math Methods in App Sciences

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“…Moreover, regarding arbitrary positive initial energy, blow up of solutions was proved. Recently, Shahrouzi in [25] investigated the blow-up result for a Lamé system of viscoelastic equation with variable-exponent nonlinearities and strong damping term.…”

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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“…They proved a blowup in finite time with negative initial energy under suitable conditions on g, f and the variable exponent of the ⃗ p(x, t)-Laplace operator. For more results regarding this matter, we refer the reader to previous studies [13][14][15][16][17][18] and the review paper. 19 Motivated by the aforementioned works, in the present paper, we study a class of elastic inverse source problem with variable-exponent nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

General decay and blow up of solutions for a class of inverse problem with elasticity term and variable‐exponent nonlinearities

Shahrouzi

2021

Math Methods in App Sciences

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In this paper, we study a class of Lamé inverse source problem with variable‐exponent nonlinearities. Under some suitable conditions on the coefficients and initial data, we proved general decay of solutions when the integral overdetermination tends to zero as time goes to infinity in appropriate range of variable exponents. Furthermore, in the absence of damping term, we show that there are solutions under some conditions on initial data and variable exponents which blow up in finite time.

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Global Nonexistence of Solutions for a Class of Viscoelastic Lamé System

Cited by 8 publications

References 21 publications

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

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

General decay and blow up of solutions for a class of inverse problem with elasticity term and variable‐exponent nonlinearities

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