<p style='text-indent:20px;'>In this paper, we consider the initial boundary value problem for a mixed pseudo-parabolic Kirchhoff equation. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions with initial energy <inline-formula><tex-math id="M1">\begin{document}$ J(u_0)\leq d $\end{document}</tex-math></inline-formula>. When the initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_0)&gt;d $\end{document}</tex-math></inline-formula>, we find another criterion for the vanishing solution and blow-up solution. Our interest also lies in the discussion of the exponential decay rate of the global solution and life span of the blow-up solution.</p>

In this paper, we consider the initial boundary value problem for a pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. Using the potential well method, we obtain a threshold result of global existence and finite-time blow-up for the weak solutions with initial energy J ( u 0 ) ≤ d . When the initial energy J ( u 0 ) > d , we find another criterion for the vanishing solution and blow-up solution. We also establish the decay rate of the global solution and estimate the life span of the blow-up solution. Meanwhile, we study the existence of the ground state solution to the corresponding stationary problem.

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Biodiesel soot particles (BSPs) and first heat-treated and then acid-treated BSPs (T-BSPs) were employed as lubricant additives for GCr15 steel/316 austenitic stainless steel contacts in aqueous media. Their tribological performances and mechanisms were tested. The result shows that T-BSPs exhibited better lubricating performances than BSPs in aqueous media. Moreover, it is proved that both BSPs and T-BSPs could enter the friction surfaces and prevent the direct steel–steel contact. In addition, T-BSPs exhibited better dispersion in water, which aided uniform adsorption on the friction surfaces, resulting in better friction-reducing and antiwear performances.

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