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math.AP2021
Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step
Panrui Ni
In this paper, we mainly focus on the existence of the viscosity solutions of \begin{equation*} \left\{ \begin{aligned} &H_1(x,Du_1(x),u_1(x),u_2(x))=0,\\ &H_2(x,Du_2(x),u_2(x),u_1…
math.AP2021★ 1 cited
A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its applications
Panrui Ni, Lin Wang, Jun Yan
Assume is a closed, connected and smooth Riemannian manifold. We consider the evolutionary Hamilton-Jacobi equation \begin{equation*} \left\{ \begin{aligned} &\partial_t u(x,t)…