Abstract
In this paper, we study the fractional p-Laplacian evolution equation with arbitrary initial energy,
$$\begin{array}{}
\displaystyle u_t(x,t) + (-{\it\Delta})_p^s u(x,t) = f(u(x,t)), \quad x\in {\it\Omega}, \,t \gt 0,
\end{array} $$
where
$\begin{array}{}
(-{\it\Delta})_p^s
\end{array} $ is the fractional p-Laplacian with
$\begin{array}{}
p \gt \max\{\frac{2N}{N+2s},1\}
\end{array} $ and s ∈ (0, 1). Specifically, by the modified potential well method, we obtain the global existence, uniqueness, and blow-up in finite time of the weak solution for the low, critical and high initial energy cases respectively.
FINITE TIME BLOW-UP AND GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR PSEUDO-PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY