On general decay for a nonlinear viscoelastic equation

ABSTRACT

This paper deals with a nonlinear viscoelastic equation. The aim is to expand the class of  the function of relaxation $h(t)$ that ensuring a general decay. We adopt the following commonly condition on relaxation function $h(t)$: $h^{\mathrm{\prime }}(t)\le -\xi (t)\chi (h(t))$, where ξ is a nonincreasing function and χ is an increasing and convex function on the whole $[0,\mathrm{\infty })$ instead of is convex only near the origin in the literature.

KEYWORDS:

• Energy decay
• multiplier technique
• wave equation
• convexity

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35B40
• 93D15
• 93D20

Disclosure statement

No potential conflict of interest was reported by the author(s).