Hamilton-Jacobi Equation: A Global Approach (Enhanced Edition‪)‬

The central problem of this book is to solve the Hamilton-Jacobi
equation
U, + H(r, X, u,) = 0,
where t is a real variable (time) and x is an R”-valued variable (space). Here
u, denotes the partial derivative with respect to time and u, the gradient in
the space variables. H is a given function of 2n + 1 real variables and a real
solution u(t, x) is sought.