On potential wells and vacuum isolating of solutions for semilinear wave equations

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A class of fourth order wave equations with dissipative and nonlinear strain terms (2008, background): “And there are only a few works on high order nonlinear evolution equations [3–31].”
Energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source (2018, background): “From the fact um(x, t) ∈ W, and combining (6) with (35), we derive ||um||2L2(Ω) < 2M.”
On solutions of space–fractional diffusion equations by means of potential wells (2016, methodology): “4), we use the potential well theory, see for examples [11,13,20,25,28] and the references therein.”