论文标题
一个空间维度中一类准粘粘性汉密尔顿 - 雅各比方程的随机均质化
Stochastic homogenization of a class of quasiconvex viscous Hamilton-Jacobi equations in one space dimension
论文作者
论文摘要
我们证明，在一个空间维度中，在固定和厄贡环境中的一类粘性汉密尔顿 - 雅各布方程均匀。 Our assumptions include most notably the following: the Hamiltonian is of the form $G(p) + βV(x,ω)$, the function $G$ is coercive and strictly quasiconvex, $\min G = 0$, $β>0$, the random potential $V$ takes values in $[0,1]$ with full support and it satisfies a hill condition that involves the diffusion coefficient.我们的方法基于表明，对于有界间隔$（θ_1（β），θ_2（β））$的每个方向，都有一个具有某些属性的唯一sublinear校正器。我们获得了有效的哈密顿量的公式，并推断出它是强制性的，相同等于$（θ_1（β），θ_2（β））$的$β$，在其他地方严格单调。
We prove homogenization for a class of viscous Hamilton-Jacobi equations in the stationary and ergodic setting in one space dimension. Our assumptions include most notably the following: the Hamiltonian is of the form $G(p) + βV(x,ω)$, the function $G$ is coercive and strictly quasiconvex, $\min G = 0$, $β>0$, the random potential $V$ takes values in $[0,1]$ with full support and it satisfies a hill condition that involves the diffusion coefficient. Our approach is based on showing that, for every direction outside of a bounded interval $(θ_1(β),θ_2(β))$, there is a unique sublinear corrector with certain properties. We obtain a formula for the effective Hamiltonian and deduce that it is coercive, identically equal to $β$ on $(θ_1(β),θ_2(β))$, and strictly monotone elsewhere.
