UNIQUENESS FOR SOLUTIONS OF NONHOMOGENEOUS A -HARMONIC EQUATIONS WITH VERY WEAK BOUNDARY VALUES

A uniqueness result for nonhomogeneous quasilinear elliptic partial differential equations with very weak boundary values was proved.

Overview of Earth-Moon Transfer Trajectory Modeling and Design

TheMoon is the only celestial body that human beings have visited.The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions.In the 21st century,new lunar missions including the construction of the lunar space station,the permanent lunar base,and the Earth-Moon transportation network have been proposed,requiring low-cost,expansive launch windows and a fixed arrival epoch for any launch date within the launch window.The low-energy and low-thrust transfers are promising strategies to satisfy the demands.This review provides a detailed landscape of Earth-Moon transfer trajectory design processes,from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods.Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp thebasic overviewof the current Earth-Moon transfer orbitdesignmethods anda deep academic background is unnecessary for the context understanding.

Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space

This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.

Singular limits for the Navier-Stokes-Poisson equations of the viscous plasma with the strong density boundary layer

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space■is rigorously proved under a Navier-slip boundary condition for velocity and the Dirichlet boundary condition for electric potential.This is achieved by establishing the nonlinear stability of the approximation solutions involving the strong boundary layer in density and electric potential,which comes from the breakdown of the quasi-neutrality near the boundary,and dealing with the difficulty of the interaction of this strong boundary layer with the weak boundary layer of the velocity field.

A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.

Strong (Weak) Exact Controllability and Strong (Weak) Exact Observability for Quasilinear Hyperbolic Systems

In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.

Trajectory optimization for the Horyu-VI international lunar mission

The Horyu-VI nano-satellite is an international lunar mission with the purpose of studying the lunar horizon glow(LHG)—a still unclear phenomenon caused by electrostatically charged lunar dust particles.This study analyzes the mission trajectory with the hypothesis that it is launched as a secondary payload of the NASA ARTEMIS-II mission.In particular,the effect of the solar gravity gradient is studied;in fact,depending on the starting relative position of the Moon,the Earth,and the Sun,the solar gradient acts differently on the trajectory—changing it significantly.Therefore,the transfer and lunar capture problem is solved in several cases with the initial Sun–Earth–Moon angle as the key parameter.Furthermore,the inclination with respect to the Moon at capture is constrained to be equatorial.Finally,the problem of stabilization and circularization of the lunar orbit is addressed in a specific case,providing an estimate of the total propellant cost to reach the final orbit around the Moon.