Geodesic
Solution of a semi-boundary-value problem for a first-order degenerate partial differential equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 48-57

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A first-order partial differential equation with constant irreversible coefficients in a Banach space is considered. In the particular case of a finite-dimensional space, the initial-boundary-value problem with irreversible matrix coefficients has no solution; hence, we pose Showalter-type conditions. Due to the regularity of the operator pencil, the equation splits into differential equations in subspaces and given conditions lead to initial conditions in subspaces. A solution to the problem is constructed and an example is provided.
Keywords: Banach space, degenerate partial differential equation, $0$-normal eigenvalue, Showalter-type conditions. 
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     author = {S. P. Zubova and A. H. Mohamad and V. I. Uskov},
     title = {Solution of a semi-boundary-value problem for a first-order degenerate partial differential equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {48--57},
     publisher = {mathdoc},
     volume = {173},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_173_a3/}
}
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S. P. Zubova; A. H. Mohamad; V. I. Uskov. Solution of a semi-boundary-value problem for a first-order degenerate partial differential equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 48-57. http://geodesic.mathdoc.fr/item/INTO_2019_173_a3/