Conservation equations can usually also be expressed in integral form: the advantage of the latter is substantially that it requires less smoothness of the solution, which paves the way to weak form, extending the class of admissible solutions to include discontinuous solutions. By integrating in any space-time domain the current density form in 1-D space: y t + j x ( y ) = 0 and by using Green's theorem, the integral form is: ∫ ∫ − − ∞ ∞ ∞ ∞ y d x + ∫ ∫ 0 ∞ ∞ j ( y ) d t = 0