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：我们展示了一种将守恒形式和Hamilton-Jacobi形式的（无粘）Burgers方程作为退化椭圆问题处理，从而获得其近似弱解方案的可行性。研究表明，不同变体能够恰当地恢复非唯一弱解，同时特定的构造性方法也可恢复相应的熵解。