Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space Yasuhiro FujitaH. IshiiPaola Loreti 35B4035F2035B2549L25Hamilton-Jacobi equationsasymptotic solutionsasymptotic behavior 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 $t \to \infty$. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2813 10.1512/iumj.2006.55.2813 en Indiana Univ. Math. J. 55 (2006) 1671 - 1700 state-of-the-art mathematics http://iumj.org/access/