Global existence of solutions to a viscoelastic non-degenerate Kirchhoff equation

ABSTRACT

In this paper, a nonlinear viscoelastic kirchhoff equation in a bounded domain with a time varying delay in the weakly nonlinear internal feedback is considered, where the global existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo–Galarkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given.

KEYWORDS:

• Global existence
• iscoelastic term
• delay term
• general decay
• convexity
• Faedo–Galarkin method

AMS CLASSIFICATION NUMBERS:

• 35L90
• 74G25
• 35B40
• 26A51

Disclosure statement

No potential conflict of interest was reported by the authors.