Geodesic
Mixed problem for a first-order partial differential equation with involution and periodic boundary conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 3-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Fourier method is used to find a classical solution of the mixed problem for a first-order differential equation with involution and periodic boundary conditions. The application of the Fourier method is substantiated using refined asymptotic formulas obtained for the eigenvalues and eigenfunctions of the corresponding spectral problem. The Fourier series representing the formal solution is transformed using certain techniques, and the possibility of its term-by-term differentiation is proved. Minimal requirements are imposed on the initial data of the problem. 
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M. Sh. Burlutskaya. Mixed problem for a first-order partial differential equation with involution and periodic boundary conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_1_a0/

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