First order PDE

Characteristics method

existence of a solution of a first order PDE

Burger equation: the crossing characteristic problem

weak derivatives/weak solution of a first order PDE/Divergence theorem

wave equations: introduction of the equation and cauchy problem

Dalambert method

Energy of a wave ed unicita' del problema di cauchy

Heat equation: definition and the Cauchy problem

Maximum porinciple/Uniqueness of the solution of the heat equation

fundamental solution and solution of the cauche problem

Laplcace equation: the stationary case of the heat equation

Classification of second order PDE