Geodesic
Properties of solutions of linear evolutionary systems with elliptic space part
Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 369-397 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the system $\mathscr L(t,x;\frac\partial{\partial t},D_x)u=f$, where $\mathscr L$ is an $N\times N$ matrix such that the matrix $\mathscr L(t,x;0,i,\sigma)$ is uniformly Petrovskii elliptic. We establish unimprovable estimates of the growth of the solutio belonging to a convex cone of the space $C^N$ in a band, in a halfspace, and in the entire space. These estimates are applied to obtain new uniqueness theorems for Cauchy's problem. Bibliography: 12 titles. 
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     author = {V. A. Kondrat'ev and S. D. \`Eidel'man},
     title = {Properties of solutions of linear evolutionary systems with elliptic space part},
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V. A. Kondrat'ev; S. D. Èidel'man. Properties of solutions of linear evolutionary systems with elliptic space part. Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 369-397. http://geodesic.mathdoc.fr/item/SM_1970_10_3_a5/

[1] V. A. Kondratev, S. D. Eidelman, “O nekotorykh svoistvakh polozhitelnykh reshenii evolyutsionnykh gipoellipticheskikh uravnenii”, DAN SSSR, 184:5 (1969), 1027–1030 | MR

[2] V. A. Kondratev, S. D. Eidelman, “O kharaktere reshenii lineinykh evolyutsionnykh sistem s ellipticheskoi prostranstvennoi chastyu”, DAN SSSR, 189:3 (1970), 468–471 | MR

[3] S. D. Eidelman, Parabolicheskie sistemy, Nauka, Moskva, 1964 | MR

[4] D. G. Aronson, “Uniquennes of positive weak solutions of second parabolic equtions”, Ann. Polon. Math., XVI (1965), 286–303 | MR

[5] D. G. Aronson, P. Besala, “Uniquenes of positive solution of parabolic equtions unbunded coefficiens”, Coll. Math., XIII (1967), 125–135 | MR

[6] I. M. Gelfand, G. E. Shilov, Prostranstva osnovnykh i obobschennykh funktsii, t. 2, Fizmatgiz, Moskva, 1958

[7] G. E. Shilov, Matematicheskii analiz (vtoroi spetsialnyi kurs), Nauka, Moskva, 1965 | MR

[8] N. N. Chaus, “Klassy edinstvennosti resheniya zadachi Koshi i predstavlenie polozhitelno opredelennykh yader”, Trudy seminara po funkts. analizu, no. 1, Institut matematiki. AN USSR, Kiev, 1968, 176–207

[9] V. S. Ryzhii, “O edinstvennosti resheniya zadachi Koshi dlya parabolicheskikh po I. G. Petrovskomu sistem s rastuschimi koeffitsientami”, Uch. zap. Kharkovskogo un-ta, 135; Зап. мех.-матем. фак. Харьковского ун-та и Харьковского матем. об-ва, 29:IV (1963), 16–22

[10] A. Fridman, Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, Moskva, 1968

[11] Mokhamed Ibragim Khasan, “Nekotorye teoremy o kachestvennom povedenii reshenii ellipticheskikh uravnenii vysshego poryadka”, Vestnik MGU, 1966, no. 2, 62–69 | Zbl

[12] Ya. B. Lopatinskii, “Povedenie reshenii lineinoi ellipticheskoi sistemy v okrestnosti izolirovannoi osoboi tochki”, DAN SSSR, 79:5 (1951), 727–730 | MR | Zbl