Mathematical results concerning a class of incompressible viscoelastic solids of differential type Academic Article

abstract

• In this paper we investigate several mathematical aspects concerning a class of incompressible viscoelastic solids of the differential type. The model that we consider can be viewed as a generalization of the KelvinVoigt viscoelastic solid. We obtain a uniqueness result and show that when the shear modulus of the viscoelastic solid is positive the solutions decay exponentially. We also show that if the shear modulus is negative, a physically unacceptable situation, we have exponential growth of the solutions, which is in keeping with physical expectations. The impossibility of localization of the solutions in finite time is also proved. The last section is devoted to the development of spatial decay estimates in the quasi-static case.

authors

• Rajagopal, Kumbakonam

published proceedings

• MATHEMATICS AND MECHANICS OF SOLIDS

author list (cited authors)

• Quintanilla, R., & Rajagopal, K. R.

citation count

• 2

complete list of authors

• Quintanilla, Ramón||Rajagopal, Kumbakonam R

publication date

• November 2011

publisher

• SAGE Publications  Publisher

published in

• Mathematics and Mechanics of Solids  Journal

keywords

• Exponential Stability
• Incompressible Viscoelastic Solids
• Spatial Behavior
• Uniqueness

Digital Object Identifier (DOI)

• 10.1177/1081286510379150

start page

• 217

end page

• 227

volume

• 16

issue

• 2