Abstract
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.
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Rodionov, A. Explicit solution for Lamé and other PDE systems. Appl Math 51, 583–595 (2006). https://doi.org/10.1007/s10492-006-0022-x
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DOI: https://doi.org/10.1007/s10492-006-0022-x