Abstract
The problem of factoring a linear partial differential operator is studied. An algorithm is designed which allows one to factor an operator when its symbol is separable, and if in addition the operator has enough right factors then it is completely reducible. Since finding the space of solutions of a completely reducible operator reduces to the same for its right factors, we apply this approach and execute a complete analysis of factoring and solving a second-order operator in two independent variables. Some results on factoring third-order operators are exhibited.
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Acknowledgments.
The paper was done during a stay of the first author at the Institut SCAI of the Fraunhofer Gesellschaft, supported by the Forschungspreis of the Humboldt Foundation which is gratefully acknowldeged. The authors are grateful to Mike Singer, Serguei Tsarev and Eckehart Hotzel for useful discussions.
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AMS Subject Classifications: 35A25, 35C05, 35G05.
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Grigoriev, D., Schwarz, F. Factoring and Solving Linear Partial Differential Equations. Computing 73, 179–197 (2004). https://doi.org/10.1007/s00607-004-0073-3
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DOI: https://doi.org/10.1007/s00607-004-0073-3