Generalized viscosity solutions for Hamilton-Jacobi equations with time- measurable Hamiltonians (Q1095302)

This paper extends the definition of viscosity solution to nonlinear first order Hamilton-Jacobi equations, \(u_ t+H(t,x,D_ xu)=0\), with time-measurable Hamiltonians, and derives a corresponding uniqueness result. The proof uses the ``blow up'' method, which removes the dependence of the Hamiltonian on (x,t). The discussion of ``blow up'' method is of substantial independent interest. The extended definition involves restricting the class of test functions used in the standard definition of viscosity solutions.