Evolution inclusions for time dependent families of subgradients

Abstract

This paper presents easy to check conditions for the existence and uniqueness of strong solutions to evolution inclusions in a Hilbert space involving a time dependent family of subgradients which are of the form

The conditions for existence and uniqueness of a solution involve an assumption of Lipshitz continuity of the convex functions rather than a Lipschitz condition on the resolvents. No smoothness is assumed on the function, f.

Keywords:

• Nonlinear evolution inclusions
• time dependent subgradients
• existence
• uniqueness

AMS:

• 34A60
• 35R70
• 35A05
• 35K20