In this paper we present a hyperbolic partial differential equation (PDE) in one space and one time dimension. This equation arose in a study of numerical schemes for simulating evolving river topographies. The solution of this PDE, whose initial data are specified along a characteristic, is very similar to that of the canonical diffusion equation. This interesting example provides insight into...

In this paper, we are concerned with the Cauchy problem and wave-breaking phenomenon for a sine-type modified Camassa-Holm (alias sine-FORQ/mCH) equation. Employing transport equations theory Littlewood-Paley theory, first establish local well-posedness strong solutions of sine-FORQ/mCH equation in Besov spaces. light Moser-type estimates, able to derive blow-up criterion precise quantity Sobol...

The application of superplastic forming for complex components manufacturing is attractive automotive and aircraft industries has been great interest in recent years. current analytical modeling theories are far from perfect this area, the results deduced it characterize conditions insufficiently well; therefore, successful numerical essential. In study, behavior novel Al-Mg-Fe-Ni-Zr-Sc alloy w...

With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are inv...

The thermo-elastic plate system of equations is analysed. The sufficient conditions of existence, uniqueness and continuity dependence on initial data of the Cauchy problem solutions for differentialoperational equation of mixed type (a part of the equation of hyperbolic type, and a part of parabolic type) are given in this paper. If the operational coefficients are suitably chosen, the investi...

In this paper we present a hyperbolic partial differential equation (PDE) in one space and one time dimension. This equation arose in a study of numerical schemes for simulating evolving river topographies. The solution of this PDE, whose initial data are specified along a characteristic, is very similar to that of the canonical diffusion equation. This interesting example provides insight into...

We show that high-dimensional analogues of the sine function (more precisely, the d-dimensional polar sine and the d-th root of the d-dimensional hypersine) satisfy a simplex-type inequality in a real preHilbert space H. Adopting the language of Deza and Rosenberg, we say that these d-dimensional sine functions are d-semimetrics. We also establish geometric identities for both the d-dimensional...