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-de...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.展开更多
基金the National Natural Science Foundation of China(11971344)Jiangsu Graduate Science Innovation Project(KYCX20-2746)。
文摘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.
