Quantitative and stability study of the evolution of a viscoelastic body

Abstract

This paper deals with a generalization of the model describing the evolution of a linear viscoelastic body studied by Kirane M. and B.S. Houari in 2011. We prove the existence and uniqueness of the solution of the model using a $C_0$-semi-group contraction method with a linear operator parameter. Moreover the strong stability of the solution is shown in a particular case.

Keywords

• viscoelasticity
• homogeneous evolution equation
• monotone maximal operator