Existence of solutions for second order evolution inclusions with application to mechanical contact problems

Abstract

In this article, we study nonlinear second order evolution inclusions defined on an evolution triple of spaces. First, we prove the existence of solutions. We introduce the integral operator, reduce the problem to the Cauchy one for a first order evolution inclusion and exploit a surjectivity result for operators which are pseudomonotone with respect to the domain of the other linear, densely defined and maximal monotone operator. Then, we give an application to a unilateral contact problem of viscoelasticity which is modeled by a dynamic hemivariational inequality.

†Dedicated to Professor N.U. Ahmed on the occasion of his 70th birthday.

Keywords:

• Hemivariational inequality
• Subdifferential
• Pseudomonotone
• Contact problem
• Friction
• Viscoelasticity

Keywords:

• Mathematics Subject Classifications 2000: 34G25
• 35L70
• 35L85
• 74H20
• 74M15

Acknowledgment

Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.

Notes

†Dedicated to Professor N.U. Ahmed on the occasion of his 70th birthday.