This paper develops a least-squares functional that arises from recasting general second-order uniformly elliptic partial differential equations in n = 2 or 3 dimensions as a system of first-order ...

The method of characteristics for solving first order quasilinear equations will be discussed. The three main types of linear second order partial differential equations will be considered: parabolic ...

Also considered are the nonlinear potential equation Δu = f (u) and the nonlinear heat equation ut – uxx = f (u). In addition, when it is applied to the equation ut + [f (u)]x = 0, we are able to ...

T6: Singularities and partial differential equations In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in ...