An approach is introduced to construct global discontinuous solutions in L~∞ for HamiltonJacobi equations. This approach allows the initial data only in L~∞ and applies to the equations with nonconvex Hamiltonians....An approach is introduced to construct global discontinuous solutions in L~∞ for HamiltonJacobi equations. This approach allows the initial data only in L~∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discoatinuous solutions in L~∞. The existence of global discontinuous solutions in L~∞ is established. These solutions in L~∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L~∞ stability of our L~∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated.展开更多
文摘An approach is introduced to construct global discontinuous solutions in L~∞ for HamiltonJacobi equations. This approach allows the initial data only in L~∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discoatinuous solutions in L~∞. The existence of global discontinuous solutions in L~∞ is established. These solutions in L~∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L~∞ stability of our L~∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated.
