论文标题
广义接触汉密尔顿 - 雅各比方程的粘度解决方案的融合
Convergence of viscosity solutions of generalized contact Hamilton-Jacobi equations
论文作者
论文摘要
对于任何紧凑的连接歧管$ m $，我们考虑在$ t^*m \ times \ times \ mathbb r $上定义的广义联系人hamiltonian $ h（x，p，u）$，它是$ p $的conex，单调增加$ u $。令$u_ε^ - ：m \ rightArrow \ mathbb r $为参数化触点的粘度解决方案hamilton-jacobi方程\ [h（x，x，x，\ partial_x u_is^ - （x），εu_im^ - （x），（x））= c（h））= c（h）$ c（h）$是Maine caligration callista crigital Valifter。 We prove that $u_ε^-$ converges uniformly, as $ε\rightarrow 0_+$, to a specfic viscosity solution $u_0^-$ of the critical equation \[ H(x,\partial_x u_0^-(x),0)=c(H) \] which can be characterized as a minimal combination of associated Peierls barrier functions.
For any compact connected manifold $M$, we consider the generalized contact Hamiltonian $H(x,p,u)$ defined on $T^*M\times\mathbb R$ which is conex in $p$ and monotonically increasing in $u$. Let $u_ε^-:M\rightarrow\mathbb R$ be the viscosity solution of the parametrized contact Hamilton-Jacobi equation \[ H(x,\partial_x u_ε^-(x),εu_ε^-(x))=c(H) \] with $c(H)$ being the Mañé Critical Value. We prove that $u_ε^-$ converges uniformly, as $ε\rightarrow 0_+$, to a specfic viscosity solution $u_0^-$ of the critical equation \[ H(x,\partial_x u_0^-(x),0)=c(H) \] which can be characterized as a minimal combination of associated Peierls barrier functions.
