This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes th...This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.展开更多
This paper discusses the null boundary controllability of two PDE's,modeling a compositesolid with different physical properties in each layer.Interface conditions are imposed.
By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one,we find for Einstein’s gravity that the variational principle works only in its submanifold w...By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one,we find for Einstein’s gravity that the variational principle works only in its submanifold with the null boundaries given by the expansion-free and shearfree hypersurfaces rather than in the whole covariant phase space.This implies that the key requirement in Harlow-Wu’s algorithm for the timelike boundaries is too restrictive for the null ones.To incorporate more generic situations into Harlow-Wu’s algorithm,we relax such a requirement.As a result,we successfully reproduce the Hamiltonian obtained previously by Wald-Zoupas’prescription for Einstein’s gravity.展开更多
基金supported by the National Natural Science Foundation of China(No.11501122)
文摘This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.
文摘This paper discusses the null boundary controllability of two PDE's,modeling a compositesolid with different physical properties in each layer.Interface conditions are imposed.
基金partially supported by the National Science Foundation of China under the Grant No.11675015,11875095,and 12075026supported in part by FWO Vlaanderen through the project G006918Nby the Vrije Universiteit Brussel through the Strategic Research Program‘High-Energy Physics’。
文摘By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one,we find for Einstein’s gravity that the variational principle works only in its submanifold with the null boundaries given by the expansion-free and shearfree hypersurfaces rather than in the whole covariant phase space.This implies that the key requirement in Harlow-Wu’s algorithm for the timelike boundaries is too restrictive for the null ones.To incorporate more generic situations into Harlow-Wu’s algorithm,we relax such a requirement.As a result,we successfully reproduce the Hamiltonian obtained previously by Wald-Zoupas’prescription for Einstein’s gravity.
