Motivated by the vanishing contact problem, we study in the present paper the convergence of solutions of Hamilton–Jacobi equations depending nonlinearly on the unknown function. Let $H(x,p,u)$ be a continuous Hamiltonian which is strictly increasing in u, and is convex and coercive in p. For each parameter $\lambda >0$, we denote by $u^{\lambda }$ the unique viscosity solution of the Hamilton–Jacobi equation

中文翻译：

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非线性取决于未知函数的Hamilton–Jacobi方程解的收敛性

受消失的接触问题的影响，我们在本文中研究了未知函数对非线性Hamilton-Jacobi方程解的收敛性。让$H（X，p，ü）$是连续的哈密顿量，在u中严格增加，在p中凸且强制。对于每个参数$\lambda >0$，我们用 ${ü}^{\lambda }$ Hamilton–Jacobi方程的唯一粘度解