一阶拟线性方程以测度为初值的BV解

分别对不带吸附项和带吸附项的一阶拟线性 方程以测度为初值的两类Cauchy问题的BV解进行了综述. 首先, 综述了上述两类Cauchy问题解的存在性、 惟一性及渐进性. 其次， 给出了在此基础上所得到的一些结果, 即上述两类方程以σ有限Borel测度为初值条件的Cauchy问题BV解的存在性、 惟一性及其他一些性质.

BV solutions for the first order quasilinear equation with local finite measure as initial value

We separately stated BV solutions for the Cauchy problems of the first order quasilinear equation and the first order quasilinear equation with source term with measure as initial value. Firstly, we displayed the general theory of above two Cauchy problems, such as existence, uniqueness and asymptotic behavior of solutions, etc. Then we displayed someresults based on it, i.e., existence, uniqueness and other properties of BV solutions for the cauchy problems of above two equations with σ-finite Borel measure as initial condition。