Removable singularities of semilinear parabolic equations

Kentaro Hirata
2013 Proceedings of the American Mathematical Society  
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 = |u| 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
more » ... ally bounded. This implies that the blow-up for continuous solutions is complete.
doi:10.1090/s0002-9939-2013-11739-9 fatcat:pcvipzwjwzdbln2ec4h2hmvrzu