A Note on Parabolic Liouville Theorems and Blow-Up Rates for a Higher-Order Semilinear Parabolic System

Abstract

We improve some results of Pan and Xing (2008) and extend the exponent range in Liouville-type theorems for some parabolic systems of inequalities with the time variable on $\mathbb{R}$. As an immediate application of the parabolic Liouville-type theorems, the range of the exponent in blow-up rates for the corresponding systems is also improved.