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Supercapacitors have been extensively studied due to their advantages of fast-charging and discharging, high-power density, long-cycling life, low cost, etc. Exploring novel nanomaterial schemes for high-performance electrode materials is of great significance. Herein, a strategy to combine vertical graphene (VG) with MoO3 nanosheets to form a composite VG/MoO3 nanostructure is proposed. VGs as transition layers supply rich active sites for the growth of MoO3 nanosheets with increasing specific surface areas. The VG transition layer further improves the electric contact and adhesion of the MoO3 electrode, simultaneously stabilizing its volume and crystal structure during repeated redox reactions. Thus, the prepared VG/MoO3 nanosheets have been demonstrated to exhibit excellent electrochemical properties, such as high reversible capacitance, better cycling performance, and high-rate capability. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the Cauchy problem for a non-linear wave equation (1)has a unique global generalized solutions in and a unique global classical solution in . We also prove that the Cauchy problem for the equation (1) admits a unique global generalized solution in C2([0, ∞); Wm, p(R) ∩ L∞(R))(m ≥ 0 is an integer,1 ≤ p ≤ ∞) and a unique global classical solution in . [ABSTRACT FROM AUTHOR]

In this paper, we prove that the Cauchy problem for the following damped generalized IMBq equation, utt-uxx-uxxtt+ν2uxxt=f(u)xx,x∈R,t>0, admits a unique global generalized solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(1≤p≤∞,m≥0) and a unique global classical solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(m>2+1p). Moreover, the blow up of the solution for the Cauchy problem of damped generalized IMBq equation is studied. We also prove that the Cauchy problem of the above-mentioned equation has a unique global generalized solution in C2([0,∞);Hs(R))(s>12) and a unique global classical solution in C2([0,∞);Hs(R))(s>52), and discuss the blow up of the solution. [ABSTRACT FROM AUTHOR]

This paper gives the sufficient conditions of blow-up of the solution of a nonlinear damped hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local generalized solution of this problem. [Copyright &y& Elsevier]

In this paper, the global existence of small amplitude solution for the Cauchy problem of the multidimensional generalized IMBq equation is proved. Moreover, we obtain a nonlinear scattering result of the Cauchy problem of the IMBq equation for small initial data. [Copyright &y& Elsevier]

In this paper, the existence and the uniqueness of the global strong solution and the global classical solution for the Cauchy problem of the multidimensional generalized IMBq equation are proved. The nonexistence of the global solution for the Cauchy problem of the generalized IMBq equation is discussed. [Copyright &y& Elsevier]