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\begin{document}

\title{FINITE TIME BLOW-UP AND GLOBAL SOLUTIONS FOR A CLASS OF FINITELY
DEGENERATE PSEUDO-PARABOLIC EQUATION}



\author[1]{Dung Huynh}%
\author[2]{Danh Pham}%
\author[3]{Tran Minh}%
\author[3]{Thi Vu}%
\affil[1]{Ho Chi Minh City University of Architecture}%
\affil[2]{University of Economics of Ho Chi Minh City}%
\affil[3]{Ho Chi Minh City University of Science}%


\vspace{-1em}



  
  \date{June 07, 2024}


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\begin{abstract}
In this paper, a class of finitely degenerate pseudo-parabolic equation,
are studied. By a potential well method, we obtain a threshold result
for the solutions to exist globally or to blow up in finite time for
sub-critical and critical initial energy. The asymptotic behavior of the
global solutions, blow-up rate, a necessary and sufficient condition for
blow-up solution, a upper bound and a lower bound for blow-up time of
local solution are also given. When the initial energy is super
critical, an abstract criterion is given for the solutions to exist
globally or to blow up in finite time, in terms of two variational
numbers. These generalize some recent results obtained in
(missing citation) and correct the proof of some results obtained by R.
Xu in (missing citation) and (missing citation)%
\end{abstract}%



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