In this paper we study the mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems in the domain D -- {（t, x） I t 〉 O, x 〉 0}. Under the assumption that the source term satisfies the ...In this paper we study the mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems in the domain D -- {（t, x） I t 〉 O, x 〉 0}. Under the assumption that the source term satisfies the matching condition, a sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.展开更多
The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global wea...The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.展开更多
For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the for...For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.展开更多
文摘In this paper we study the mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems in the domain D -- {（t, x） I t 〉 O, x 〉 0}. Under the assumption that the source term satisfies the matching condition, a sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.
基金Project supported by the Special Funds for Major State Basic Research Projects of China
文摘The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.
基金Supported by the National Natural Science Foundation of China(Grant No.10926162)the Fundamental Research Funds for the Central Universities(Grant No.2009B01314)the Natural Science Foundation of HohaiUniversity(Grant No.2009428011)
文摘For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.
