By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o...By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.展开更多
Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is prove...Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:展开更多
文摘By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.
文摘Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:
