TY - JOUR T1 - Solving Inhomogeneous Linear Partial Differential Equations AU - Fritz Schwarz JO - Journal of Partial Differential Equations VL - 4 SP - 374 EP - 388 PY - 2010 DA - 2010/11 SN - 23 DO - http://doi.org/10.4208/jpde.v23.n4.5 UR - https://global-sci.org/intro/article_detail/jpde/5240.html KW - Partial differential equations KW - linear differential equations KW - inhomogeneous differential equations AB -

Lagrange's variation-of-constantsmethod for solving linear inhomogeneous ordinary differential equations (ode's) is replaced by amethod based on the Loewy decomposition of the corresponding homogeneous equation. It uses only properties of the equations and not of its solutions. As a consequence it has the advantage that it may be generalized for partial differential equations (pde's). It is applied to equations of second order in two independent variables, and to a certain system of third-order pde's. Therewith all possible linear inhomogeneous pde's are covered that may occur when third-order linear homogeneous pde's in two independent variables are solved.