TY - JOUR
T1 - A Priori Bounds for Global Solutions of Higher-order Semilinear Parabolic Problems
JO - Journal of Partial Differential Equations
VL - 3
SP - 221
EP - 233
PY - 2008
DA - 2008/08
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5279.html
KW - A priori bound
KW - higher-order equation
KW - semilinear parabolic problem
KW - maximal regularity estimate
AB -  In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal regularity estimates. If n ≥ \frac{10}{3}m, we also give another proof which does not use maximal regularity estimates.