Multiplication of solutions for linear overdetermined systems of partial differential equations |
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Authors: | Jens Jonasson |
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Affiliation: | Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden |
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Abstract: | A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE’s contains the Cauchy–Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebraic way, large classes of non-trivial solutions that can be constructed by forming convergent power series of trivial solutions. |
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Keywords: | 35F05 35N10 58J99 |
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