Global solutions to semilinear subdiffusion-normal transport equations: well-posedness and Strichartz estimates

Abstract

This paper is concerned with a class of time-fractional subdiffusion-normal transport equations that describe the transition from subdiffusion to normal diffusion. Our primary contribution is the establishment of the well-posedness and Strichartz estimates for global solutions on the unbounded domain RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb R^N$$\end{document}. Furthermore, we extend our analysis to bounded domains with smooth boundaries, proving well-posedness and Strichartz estimates for small initial data and under the condition of a polynomial growth nonlinearity.