Title: Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space

Authors: Yasuhiro Fujita, Hitoshi Ishii and Paola Loreti

Issue: Volume 55 (2006), Issue 5, 1671-1700

Abstract: We study the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation $u_{t} + \alpha x \cdot Du + H(Du) = f(x)$ in $\mathbb{R}^{n} \times (0,\infty)$, where $\alpha$ is a positive constant and $H$ is a convex function on $\mathbb{R}^{n}$, and establish a convergence result for the viscosity solution $u(x,t)$ as $t \to \infty$.