Triebel-Lizorkin Space Estimates for Evolution Equations with Structure Dissipation

Ms. Jingchun Chen
University of Wisconsin-Milwaukee
PhD Graduate Student

“The goal of this dissertation is to get the long time decay estimates of the generalized heat equations and the generalized wave equations in the homogeneous Triebel-Lizorkin spaces. We first extend the known results for the generalized heat equations in the real Hardy spaces. We also extend the known results for the generalized wave equations with structure dissipation in the real Hardy spaces. Our main tools are the decomposition of the unit, duality property in Triebel-Lizorkin spaces and the multiplier theorems in different function spaces such as Lebesuge spaces, real Hardy spaces and Triebel-Lizorkin spaces.”

Committee Members:
Profs. Lijing Sun (Advisor); Kevin McLeod, Gabriella Pinter, Hans Volkmer, & Jeb Willenbring