The Fourier method for the linear partial differential equations of the \(n\)-th order. (English) Zbl 0706.35036

Hančl, Jaroslav

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 28, 123-135 (1989).

This paper describes solutions of linear partial differential equations of the type \[ \sum^{n}_{k=0}a_ k(t)\partial^ ku/\partial t^ k=\sum^{n}_{k=0}b_ k(y)\partial^ ku/\partial y^ k \] using the combination of the Fourier method and Kummer transformation. The coefficients \(a_ k(t)\) and \(b_ k(y)\) must fulfil further conditions.

Reviewer: J.Hančl

MSC:

35G05	Linear higher-order PDEs
35A22	Transform methods (e.g., integral transforms) applied to PDEs
35C05	Solutions to PDEs in closed form

Keywords:

Fourier method; Kummer transformation

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