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Global existence and nonexistence of strong solutions to pseudo-parabolic equations with variable exponents
  • Le Nhan,
  • Truong Le
Le Nhan
Ho Chi Minh City University of Technology and Education
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Truong Le
University of Economics Ho Chinh Minh City
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Abstract

This paper deals with a pseudo-parabolic equation involving variable exponents under Dirichlet boundary value condition. The authors first develop the potential well method to prove a threshold result on the existence and nonexistence of global solutions to the equations when initial energy is less than the mountain pass level $d$. By borrowing the idea from \cite{GW05,XS13} we also show some existence and nonexistence results with high energy initial data. In this case a new characterization for nonexistence of solution is given. These results extend and improve a recent result obtained by Di et al. (2017) \cite{DSP17} and Liao (2019) \cite{Liao19,LGL19}.