Discontinuous solutions in L ∞ for Hamilton-Jacobi equations - Guiqiang, C; Bo, S (Kluwer Academic Publishers, 2000)
An approach is introduced to construct global discontinuous solutions in L ∞ for Hamilton-Jacobi 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 discontinuous 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. © 1983 Shanghai Scientific and Technological Literature Publishing House.