arXiv subjects
Publications and source records attributed to Wenjun Liu.
By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson's rules, but also give some new error bounds for other quadrature rules as special cases. Especially, two sharp error inequalities are derived when n is an odd and an even integer, respectively.
The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential.
In this paper we consider the viscoelastic wave equation of Kirchhoff type: $$ u_{tt}-M(\|\nabla u\|_{2}^{2})Δu+\int_{0}^{t}g(t-s)Δu(s){\rm d}s+u_{t}=|u|^{p-1}u $$ with Dirichlet boundary conditions. Under some suitable assumptions on $g$ and the initial data, we established a global nonexistence result for certain solutions with arbitrarily high energy.
In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral type inequalities on time scales as special cases.
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.
In this paper we derive a new inequality of Ostrowski-Gruss type on time scales and thus unify corresponding continuous and discrete versions. We also apply our result to the quantum calculus case.