Removable singularities of semilinear parabolic equations

Abstract

This paper extends the recent result due to Hsu (2010) about removable singularities of semilinear parabolic equations. Our result is applicable to solutions of equations of the form ∆u + @tu = juj p 1 u with 0 p < n=(n 2). The proof is based on the parabolic potential theory and an iteration argument. Also, we prove that if 0 < p < (n + 2)=n, then integral solutions of semilinear parabolic equations with nonlinearity depending on space and time variables and u p are locally bounded. This implies that the blow-up for continuous solutions is complete.