Geodesic
Passive linear systems of partial differential equations
Sbornik. Mathematics, Tome 44 (1983) no. 3, pp. 269-278 
Yu. N. Drozhzhinov. Passive linear systems of partial differential equations. Sbornik. Mathematics, Tome 44 (1983) no. 3, pp. 269-278. http://geodesic.mathdoc.fr/item/SM_1983_44_3_a1/
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     author = {Yu. N. Drozhzhinov},
     title = {Passive linear systems of partial differential equations},
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     year = {1983},
     volume = {44},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_3_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the concept of a system passive relative to a cone that was introduced by V. S. Vladimirov for the case of translation-invariant systems is extended to systems which are not translation invariant. For systems of linear partial differential equations of first order with variable coefficients necessary and sufficient conditions are found for them to be passive relative to a cone. A generalized Cauchy problem is posed for such systems, and it is proved that this problem is well posed under the condition of strict nondegeneracy. Bibliography: 7 titles.

[1] Zemanian A., Distribution theory and transform analysis, McGraw-Hill, 1965 | MR | Zbl

[2] Beltrami E., Wohlers M., Distributions and the boundary values of analytic functions, N. Y., London, 1966 | MR

[3] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[4] Friedrichs K., “Symmetric Positiv Linear Differential Equations”, Comm. pure and Appl. Math., 11 (1958), 333–418 | DOI | MR | Zbl

[5] Lax P., Phillips R., “Local Boundary Conditions for Dissipative Symmetric linear differential Operators”, Comm. pure and Appl. Math., 13 (1960), 427–455 | DOI | MR | Zbl

[6] Friedrichs K., “Symmetric Hyperbolic Linear differential Equations”, Comm. pure and Appl. Math., 7 (1954), 345–392 | DOI | MR | Zbl

[7] Danford N., Shvarts D., Lineinye operatory. Spektralnaya teoriya, Mir, M., 1966