论文标题
汉密尔顿 - 雅各比方程的单调系统的消失折扣问题：完全融合的反例
The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: a counterexample to the full convergence
论文作者
论文摘要
近年来，对汉密尔顿 - 雅各比方程的消失折扣问题引起了极大的兴趣。在标量方程式的情况下，B。Ziliotto最近给出了一个示例的示例，其中梯度变量中具有非凸hamiltonian的Hamilton-Jacobi方程，该溶液的完整收敛性并不成立，因为折现因子倾向于零。我们在这里给出了一个明确的示例，它的汉密尔顿 - 雅各布方程的非线性单调系统在梯度变量中具有凸汉密尔顿人，因此解决方案的完整收敛失败了，因为折现因子为零。
In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian in the gradient variable, for which the full convergence of the solutions does not hold as the discount factor tends to zero. We give here an explicit example of nonlinear monotone systems of Hamilton-Jacobi equations having convex Hamiltonians in the gradient variable, for which the full convergence of the solutions fails as the discount factor goes to zero.
