Geodesic
On a spectral problem for a system of~differential equations of mixed type
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 4, pp. 611-632

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This article explores the spectral characteristics of the differential operator generated by the boundary problem for linear systems of differential equations of mixed type. The simplest example of a classical system of equations that falls within the field of our consideration is the system of equations of mixed type: $$D_tu_1-{\rm sign}D_xu_2-\varepsilon u_2=f_1, \quad D_tu_2+D_xu_1+\varepsilon u_1=f_2$$ Elliptic for $t>0$ and hyperbolic for $t0$.
Keywords: boundary-value problems, the spectrum of the operator of the system of differential equations, periodic problems, the system of equations of mixed type, basis. 
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     author = {D. V. Kornienko},
     title = {On a spectral problem for a system of~differential equations of mixed type},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {611--632},
     publisher = {mathdoc},
     volume = {21},
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     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2017_21_4_a1/}
}
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D. V. Kornienko. On a spectral problem for a system of~differential equations of mixed type. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 4, pp. 611-632. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_4_a1/