TY - JOUR
T1 - Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians
AU - Ichihara, Naoyuki
AU - Ishii, Hitoshi
PY - 2009/9
Y1 - 2009/9
N2 - We investigate the long-time behavior of viscosity solutions of Hamilton-Jacobi equations in ℝn with convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples. We take a dynamical approach, based on tools from weak KAM theory such as extremal curves, Aubry sets and representation formulas for solutions, for these investigations.
AB - We investigate the long-time behavior of viscosity solutions of Hamilton-Jacobi equations in ℝn with convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples. We take a dynamical approach, based on tools from weak KAM theory such as extremal curves, Aubry sets and representation formulas for solutions, for these investigations.
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U2 - 10.1007/s00205-008-0170-0
DO - 10.1007/s00205-008-0170-0
M3 - Article
AN - SCOPUS:70349498824
SN - 0003-9527
VL - 194
SP - 383
EP - 419
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -