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• W2013288539 abstract "It is shown that solutions to a class of diffusion equations of the two-way type may be found by a method akin to separation of variables. The difficulty with such equations is that the boundary data must be specified partly as initial and partly as final conditions. In contrast to the one-way diffusion equation, where the solution separates only into decaying eigenfunctions, the two-way equations separate into both decaying and growing eigenfunctions. Criteria are set forth for the existence of linear eigenfunctions, which may not be found directly by separating variables. A speculation with interesting ramifications is that the growing and decaying eigenfunctions are separately complete in an appropriate half of the problem domain. This conjecture is not proved, although it does enjoy some numerical support." @default.
• W2013288539 created "2016-06-24" @default.
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• W2013288539 date "1980-04-01" @default.
• W2013288539 modified "2023-09-29" @default.
• W2013288539 title "Separating variables in two-way diffusion equations" @default.
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• W2013288539 doi "https://doi.org/10.1063/1.524495" @default.
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