Generalized frameworks for first-order evolution inclusions based on Yosida approximations

Abstract

First, general frameworks for the first-order evolution inclusions are developed based on the A-maximal relaxed monotonicity, and then using the Yosida approximation the solvability of a general class of first-order nonlinear evolution inclusions is investigated. The role the A-maximal relaxed monotonicity is significant in the sense that it not only empowers the first-order nonlinear evolution inclusions but also generalizes the existing Yosida approximations and its characterizations in the current literature.

Keywords

• Generalized first-order evolution inclusions
• variational problems
• maximal monotone mapping
• A-maximal relaxed monotone mapping
• generalized resolvent operator
• general Yosida approximations