TY  - INPR
A1  - De-Xing, Kong
A1  - Hui, Yao
T1  - Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws II
N2  - In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate fields. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C¹ functions. In particular, the authors give the optimal control time of the system. Finally, a new application is also given.
T3  - Preprint - (2003) 08 
KW  - Quasilinear hyperbolic system
KW  - conservation laws
KW  - global exact boundary controllability
KW  - Cauchy problem
KW  - Goursat problem
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26565
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Wafo, Roger Tagne
T1  - Initial value problems for wave equations on manifolds
JF  - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics
N2  - We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hormander.
KW  - Wave equation
KW  - Globally hyperbolic Lorentz manifold
KW  - Cauchy problem
KW  - Goursat problem
KW  - Finite energy sections
Y1  - 2015
U6  - https://doi.org/10.1007/s11040-015-9176-7
SN  - 1385-0172
SN  - 1572-9656
VL  - 18
IS  - 1
PB  - Springer
CY  - Dordrecht
ER  -