The initial-boundary value problem for a system of nonlinear elastic waves

我们研究了F.John提出的球对称解的初边值问题，其中边界是球面。对于球对称解，我们给出了具体的非线性边界条件，即牵引力问题。作为通向非线性问题的第一步，我们证明了对于任何材料，线性初边值问题的能量不等式在内域和外域都成立。

We studied the initial-boundary problem for spherical symmetric solutions introduced by F.John, where boundary is a sphere. We formulated concretely nonlinear boundary condition so called traction problem for spherical symmetric solution. As the first step toward to nonlinear problem, we established that the energy inequalities for linear initial-boundary problem hold in the interior and exterior domain for any material.