Qualitative analysis of solutions for the p‐Laplacian hyperbolic equation with logarithmic nonlinearity

Abstract

In this paper, the p‐Laplacian hyperbolic type equation with logarithmic nonlinearity and weak damping term are considered, where the global existence of solutions by using the potential well method is discussed. Furthermore, the growth and the decay estimates of solutions for the problem are studied.

Global Existence and Decay Estimates of Energy of Solutions for a New Class of p -Laplacian Heat Equations with Logarithmic Nonlinearity

“…Various dynamical systems in physics and engineering are also modeled by using evolutionary differential equations. Many researchers have contributed a lot to provide an outstanding history of the evolutionary differential partial equations related to pðxÞ-Laplacian such as [13][14][15][16][17].…”

“…Motivated by the last mentioned papers, especially [14], in this current research, we consider problem (1) with the presence of nonlinear diffusion Δ p = div ðj∇uj p−2 ∇uÞ, logarithmic nonlinearity juj p−2 u ln juj together with a damping term which is an extension of the previous recent analytical study in [14], where the authors considered the hyperbolic case without damping terms. Our goal is to exploit a potential well method for problem (1) in order to obtain global existence and decay estimate of solutions.…”

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

“…The same is said for the evolutionary partial differential equations associated with pðxÞ-Laplacian (see [8,14,15]).…”

“…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].…”

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

“…Viscoelasticity is included in the study of biological materials. A viscoelastic material will return to its original shape after any deforming force has been removed even though it will take time to do so (see previous studies) 1‐12 …”