论文标题
汉密尔顿 - 雅各比方程的单调系统消失的折扣问题的一个例子
An example in the vanishing discount problem for monotone systems of Hamilton-Jacobi equations
论文作者
论文摘要
近年来，汉密尔顿 - 雅各比方程的消失折扣问题有很多贡献。在标量方程式的情况下，B。Ziliotto[折扣汉密尔顿 - 雅各比方程的解决方案的收敛：反例。 J. Math。 Pures Appl。 （9）128（2019），330-338]展示了一个在梯度变量中具有非Convex Hamiltonian的Hamilton-Jacobi方程的示例，因为该方案的全部收敛性并不成立，因为折现因子往往为零。我们举例说明汉密尔顿 - 雅各比方程的非线性单调系统在梯度变量中具有凸汉密尔顿的汉密尔顿方程，为此，整个家庭的融合都不成立。
In recent years, there have been many contributions to the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto [Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexample. J. Math. Pures Appl. (9) 128 (2019), 330-338] has shown 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 an example of the nonlinear monotone system of Hamilton-Jacobi equations having convex Hamiltonians in the gradient variable, for which the whole family convergence of the solutions does not hold.
