The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a funct...The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.展开更多
MORE than 10 years ago, the song Come Home As Often As You Can to See Your Parents became popular in China, reminding young people of their obli- gation to set aside their hectic lives and return to their hometowns to...MORE than 10 years ago, the song Come Home As Often As You Can to See Your Parents became popular in China, reminding young people of their obli- gation to set aside their hectic lives and return to their hometowns to visit their aging parents. Today, the idea expressed in this song has been codified in Chinese law.展开更多
Numerical solutions of Riemann problems for 2-D scalar conservation law are given by a second order accurate MmB (locally Maximum-minimum Bounds preserving) scheme which is non-splitting. The numerical computations s...Numerical solutions of Riemann problems for 2-D scalar conservation law are given by a second order accurate MmB (locally Maximum-minimum Bounds preserving) scheme which is non-splitting. The numerical computations show that the scheme has high resolution and non-oscillatory properties. The results are completely in accordance with the theoretical solutions and all cases are distinguished efficiently展开更多
This paper considers the simultaneous attack problem of multiple missiles against a maneuvering target. Different from most of the existing literature in which the simultaneous attack problem is formulated as a consen...This paper considers the simultaneous attack problem of multiple missiles against a maneuvering target. Different from most of the existing literature in which the simultaneous attack problem is formulated as a consensus problem of missiles＇ time-to-go estimates, this paper formulates it as the consensus problem of missiles＇ ranges-to-go. Based on this strategy, novel distributed guidance laws are proposed to solve the simultaneous attack problem with the target of unknown maneuverability.Adaptive control method is introduced to estimate the upper bound of the target＇s acceleration. The effectiveness of the proposed guidance laws is verified both theoretically and numerically.展开更多
In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a ...In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a system of variational inequalities on the boundary of the given domain. The existence and uniqueess of this system are established for a small frictional coefficient. The boundary element approximation of this system is presented and an error estimate is given.展开更多
We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we dis...We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.展开更多
基金supported by the PRIN 2012 project Nonlinear Hyperbolic Partial Differential Equations,Dispersive and Transport Equations:Theoretical and Applicative Aspectsthe INDAM–GNAMPA 2014 project Conservation Laws in the Modeling of Collective Phenomena
文摘The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.
文摘MORE than 10 years ago, the song Come Home As Often As You Can to See Your Parents became popular in China, reminding young people of their obli- gation to set aside their hectic lives and return to their hometowns to visit their aging parents. Today, the idea expressed in this song has been codified in Chinese law.
文摘Numerical solutions of Riemann problems for 2-D scalar conservation law are given by a second order accurate MmB (locally Maximum-minimum Bounds preserving) scheme which is non-splitting. The numerical computations show that the scheme has high resolution and non-oscillatory properties. The results are completely in accordance with the theoretical solutions and all cases are distinguished efficiently
基金supported by the National Natural Science Foundation of China under Grant Nos.61473005,11332001,and 61471242the Research Project Fund under Grant No.17-163-11-ZT-003-018-01+2 种基金the Air Force Advance Research Fund under Grant No.303020503the Joint Fund of Equipment development and Aerospace Science and Technology under Grant No.6141B0624050101the National Defense Basic Scientific Research Program(Major)of China
文摘This paper considers the simultaneous attack problem of multiple missiles against a maneuvering target. Different from most of the existing literature in which the simultaneous attack problem is formulated as a consensus problem of missiles＇ time-to-go estimates, this paper formulates it as the consensus problem of missiles＇ ranges-to-go. Based on this strategy, novel distributed guidance laws are proposed to solve the simultaneous attack problem with the target of unknown maneuverability.Adaptive control method is introduced to estimate the upper bound of the target＇s acceleration. The effectiveness of the proposed guidance laws is verified both theoretically and numerically.
文摘In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a system of variational inequalities on the boundary of the given domain. The existence and uniqueess of this system are established for a small frictional coefficient. The boundary element approximation of this system is presented and an error estimate is given.
基金This work is supported by Thales Alenia Space.We are gratefully indebted to J.-F.Coulombel,F.GolseK.Aoki for many useful advices concerning this work and for their kind encouragements。
文摘We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.
