General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping, logarithmic nonlinearity and distributed delay terms

Abstract

In this paper, we consider a nonlinear viscoelastic Kirchhoff equation with the presence of both distributed delay term, Balakrishnan‐Taylor damping, and logarithmic nonlinearity. We describe a exponential decay of solutions, and we obtained the asymptotic stability result of the global solution. This study is a continuation of Boulaaras's works (Math. Meth. Appl. Sci. 2019;42:4795– 4814 and Alex. Eng. J. 2020;59:1059–1071)

Nonlinear Models of Thermo-Viscoelastic Materials

“…In addition, we assume that η is continuous while ψ is continuously differentiable. Upon evaluation of ψ and substitution in (7), we obtain…”

“…The memory effects of viscoelasticity are modeled jointly with thermal properties. In this respect, we observe that dissipative properties are ascribed to the materials models; there are approaches or models where dissipative effects are associated with external damping or boundary conditions [7].…”

Blow‐up and decay of solutions for a viscoelastic Kirchhoff‐type equation with distributed delay and variable exponents

“…in which q − = ess inf z∈Ω q(z), q + = ess sup Of course, we consider the well-known Kirchhoff-type equation developed by Kirchhoff in the year 1876 [1] for further investigation, which is concerned with the study to describe small vibration amplitude of elastic stings, see [2][3][4]. We mix some types of damping such as the variable exponent, viscoelastic damping, distributed delay, and source terms.…”

Blowing Up for the p -Laplacian Parabolic Equation with Logarithmic Nonlinearity

“…And for more information on some of the other works to which this term was introduced, we refer the reader to [13,14,[16][17][18][19][20][21][22][23][24].…”