A PDE Approach to the Long-Time Asymptotic Solutions of Contact Hamilton-Jacobi Equations  

作　　者：WANG Yujie LI Xia 

机构地区：[1]School of Mathematics Science,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China

出　　处：《Wuhan University Journal of Natural Sciences》2022年第3期189-194,共6页武汉大学学报（自然科学英文版）

基　　金：the National Natural Science Foundation of China(11971344);Jiangsu Graduate Science Innovation Project(KYCX20-2746)。

摘　　要：We study the long-time asymptotic behaviour of viscosity solutions u(x,t)of the Hamilton-Jacobi equation u_(t)(x,t)+H(x,u(x,t),Du(x,t))=0 in T^(n)×(0,∞)with a PDE approach,where H=H(x,u,p)is coercive in p,non-decreasing in u and strictly convex in(u,p),and establish the uniform convergence of u(x,t)to an asymptotic solution u_(∞)(x)as t→∞.Moreover,u_(∞) is a viscosity solution of Hamilton-Jacobi equation H(x,u(x),Du(x))=0.

关 键 词：asymptotic solution Hamilton-Jacobi equation PDE approach 

分 类 号：O193[理学—数学]