A computational approach for the analytical solving of a Dirichlet-type problem for third order partial differential equations (Q1406065)

Consider a domain \(\Omega= \{(x,\phi); x\in D\subset \mathbb{R}^2, \phi\in(0, 2\pi)\}\), and the differential operator \[ A= \Biggl({\partial^2\over \partial p\partial\phi}\Biggr) \Biggl[\sin(\phi)\Biggl({\partial\over\partial x_1}\Biggr)+ \cos(\phi)\Biggl({\partial\over\partial x_2}\Biggr)\Biggr];\;\Biggl({\partial\over\partial p}\Biggr)= \cos(\phi)\Biggl({\partial\over\partial x_1}\Biggr)- \sin(\phi)\Biggl({\partial\over\partial x_2}\Biggr). \] The problem is to find an approximated solution \(u\) of the inverse problem \[ Au(x,\phi)= F(x,\phi),\quad\forall(x,\phi)\in \Omega,\quad u(x,\phi)|_{\delta D\times (0,2\pi)}= 0. \] When \(D\) is the unit disk of \(\mathbb{R}^2\), the authors give an algorithm, using MAPLE.