Fujita type results for a class of degenerate parabolic operators
Andrea Pascucci · Advances in Differential Equations · 1999
In this paper we study the global existence of non-negative solutions to the Cauchy problem for $Lu= - u^{p}$ where $L$ belongs to a class ${\cal L}$ of hypoelliptic operators of degenerate parabolic type and $p>1$. Extending some old results by Fujita, we prove the existence and we determine explicitly a critical exponent $p^{*}$ for the problem. Namely, we prove that if $p>p^{*}$ then there are global positive solutions to the problem, while if $1 <p