Global existence of solutions for the system of compressible adiabatic flow through porous media
Global existence of solutions for the system of compressible adiabatic flow through porous media
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DOI：
10.1137/s0036141094267078
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发表时间：
1996
影响因子：
2
通讯作者：
L. Hsiao;D. Serre
中科院分区：
文献类型：
--
作者：
L. Hsiao;D. Serre
考虑拟线性双曲方程组\[（1）\qquad \left\{ \开始{gathered} v_t - u_x = 0，\hfill \\ u_t + p（v，s）_x = - \alpha u，\quad \alpha > 0，\quad p_v 0，\hfill \\ s_t = 0 \hfill \ \end{gathered} \right.\]初始数据\[（2）\qquad u（x，0）= u_0（x），\quad v（x，0）= \bar v + v_o（x），\quad s（x，0）= \bar s + s_0（x），\]其中$\bar v > 0$，$\bar v$和$\bar s$是常数，$（u_0（x），v_0（x））\在具有紧凑支持的C^1 $中，证明了当$（u_0（x），v_0（x））$的C^1 $-范数和$s_0（x）$的C^2 $-范数都很小时，Cauchy问题存在整体经典解.
Consider the quasilinear hyperbolic system \[(1)\qquad \left\{ \begin{gathered} v_t - u_x = 0, \hfill \\ u_t + p(v,s)_x = - \alpha u,\quad \alpha > 0,\quad p_v 0, \hfill \\ s_t = 0 \hfill \\ \end{gathered} \right.\] with initial data \[ (2)\qquad u(x,0) = u_0 (x),\quad v(x,0) = \bar v + v_o (x),\quad s(x,0) = \bar s + s_0 (x), \] where $\bar v > 0$, $\bar v$ and $\bar s$ are constants, $(u_0 (x),v_0 (x)) \in C^1 $ with a compact support, and $s_0 (x) \in C^2 $ with a compact support.It is proved in this paper that there exists a globally defined classical solution for the Cauchy problem if the $C^1 $-norm of $(u_0 (x),v_0 (x))$ and the $C^2 $-norm of $s_0 (x)$ are small.