Higher-order Integrability For A Semilinear Heat Equation On Time-varying Domain

The main purpose of this dissertation is to establish some higher-order in-tegrability near the initial time for the solutions of a heat equation defined on a time-varying domain. Based on the existence of solutions that obtained in K-loeden et al.[21], we first deduce some a priori estimates for the approximation solutions, and then obtain the higher-order integrability near the initial time for the weak solutions.