We demonstrate the feasibility of a scheme to obtain approximate weak solutions to the (inviscid) Burgers equation in conservation and Hamilton-Jacobi form, treated as degenerate elliptic problems. We show different variants recover non-unique weak solutions as appropriate, and also specific constructive approaches to recover the corresponding entropy solutions.

翻译：我们论证了一种方案的有效性，该方案将守恒形式与Hamilton-Jacobi形式下的（无粘）Burgers方程作为退化椭圆问题处理，从而获取其近似弱解。研究表明，不同变体可恰当地恢复非唯一弱解，并提出了恢复相应熵解的具体构造方法。