Bidimensional Problems
F. G. Aliev, Antonio Lara · 2023
This chapter describes in a detailed manner the solutions of different problems in confined systems in two dimensions in Cartesian coordinates. The solutions will be sought by using the method of separation of variables, as functions of two (for example for static Laplace or Poisson problems) or three variables in the case of wave or diffusion problems (when time is considered). The separation of variables will be performed in order to expand the solution in orthogonal functions in one or two dimensions. In the case of converting the initial problem in several simpler problems the authors need to take care that the Laplace problem with all boundaries of homogeneous type has trivial solution (zero or a constant). In several cases the intermediate solutions will be analyzed graphically, whereas the final solutions will be presented using the PDE tool from MATLAB.