Generalized first-order nonlinear evolution equations and generalized Yosida approximations based on H-maximal monotonicity frameworks

Abstract

First a general framework for the Yosida approximation is introduced based on the relative H-maximal monotonicity model, and then it is applied to the solvability of a general class of first-order nonlinear evolution equations. The obtained results generalize and unify a wide range of results to the context of the solvability of first-order nonlinear evolution equations in several settings.

Keywords

• Generalized first-order evolution equations
• variational problems
• maximal monotone mapping
• relative H-maximal monotone mapping
• relative H-maximal accretive mapping
• generalized resolvent operator
• general Yosida approximations