Partial differential equations with non-homogenous boundary conditions

Abstract

Boundary value problems of partial differential equations are very often solved by the method of «separation of variables» or Fourier method. The method can be used without any difflculty in homogenous problems, that is, in prohlems where de differential equation and the boundary conditions are homogenous. Most of the textbooks concentrate their attention on such problems and for the inhomogenous case they merely' suggest using an integral transform procedure. Nevertheless the Fourier method may be extented to treat the inhomogenous problems. A recent text by Tolstov (see reference 1), treats the case when the differential equation is not homogenous but not the case when the boundary conditions are also inhomogenous. Kaplan (see reference 2), in his Advanced Calculus treats relatively simple cases of inhomogenous boundary conditions.