带有非负非线性源的拟线性双曲方程BV解的存在唯一性

Existence and uniqueness of BV solution for a quasilinear hyperbolic equation with nonnegative nonlinear source

主要研究了一类带有非负的非线性源的拟线性双曲守恒律方程的Cauchy问题,其中初值为有限Borel测度.克服了初值和非线性项带来的阻碍,得到了局部BV解的存在唯一性.

In this paper, the Cauchy problem of quasilinear hyperbolic conservation law equations with nonnegative nonlinear sources is studied. The initial value is the finite Borel measure. By overcoming the obstacles caused by initial values and nonlinear terms, the existence and uniqueness of local BV solutions are obtained.