DISCONTINUOUS SOLUTIONS IN L~∞ FOR HAMILTON-JACOBI EQUATIONS  

作　　者：CHENGUIQIANG SUBo 

机构地区：[1]：DepartmentofMathematics,NorthwesternUniversity,2033SheridanRoad,Evanston,IL60208-2730,USA [2]DepartmentofMathematics,UniversityofWisconsinatMadison,Madison,WI53706-1380,USA.

出　　处：《Chinese Annals of Mathematics,Series B》2000年第2期165-186,共22页数学年刊（B辑英文版）

基　　金：National Science Foundation!DMS-9971793;National Science Foundation!DMS-9708261

摘　　要：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.

关 键 词：Hamilton-Jacobi equations Discontinuous solutions Profit functions Viscosity solutions Madman solutions STABILITY 

分 类 号：O175.2[理学—数学]