Geodesic
On the Unique Continuation of the Germs of Solutions of First-Order Differential Equations along Curves
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 917-930.

Voir la notice de l'article provenant de la source Math-Net.Ru

For solutions of linear, weakly nonlinear, and quasilinear first-order differential equations, we obtain theorems on the unique unbounded continuation of germs along continuous curves contained in the integral submanifolds of the distribution induced by the major part of the equation.
Keywords: germs of solutions, unique definiteness of germs.
Mots-clés : unique continuation 
@article{MZM_2017_102_6_a11,
     author = {N. A. Shananin},
     title = {On the {Unique} {Continuation} of the {Germs} of {Solutions} of {First-Order} {Differential} {Equations} along {Curves}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {917--930},
     publisher = {mathdoc},
     volume = {102},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a11/}
}
TY  - JOUR
AU  - N. A. Shananin
TI  - On the Unique Continuation of the Germs of Solutions of First-Order Differential Equations along Curves
JO  - Matematičeskie zametki
PY  - 2017
SP  - 917
EP  - 930
VL  - 102
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a11/
LA  - ru
ID  - MZM_2017_102_6_a11
ER  - 
%0 Journal Article
%A N. A. Shananin
%T On the Unique Continuation of the Germs of Solutions of First-Order Differential Equations along Curves
%J Matematičeskie zametki
%D 2017
%P 917-930
%V 102
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a11/
%G ru
%F MZM_2017_102_6_a11
N. A. Shananin. On the Unique Continuation of the Germs of Solutions of First-Order Differential Equations along Curves. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 917-930. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a11/

[1] M. Strauss, F. Trèves, “First-order linear PDEs and uniqueness in the Cauchy problem”, J. Differential Equations, 15 (1974), 195–209 | DOI | MR | Zbl

[2] F. Cardoso, J. Hounie, “First-order linear PDEs and uniqueness in the Cauchy problem”, J. Differential Equations, 33:2 (1979), 239–248 | DOI | MR | Zbl

[3] S. Alinhac, “Non-unicité du probleme de Cauchy pour des operateurs de type principal”, Sémin. Goulaouic–Meyer–Schwartz, Exp. No. 16, École Polytech., 1981 | Zbl

[4] N. A. Shananin, “Ob odnoznachnom prodolzhenii reshenii differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. sb., 191:3 (2000), 113–142 | DOI | MR | Zbl

[5] N. A. Shananin, “O chastichnoi kvazianalitichnosti obobschennykh reshenii slabo nelineinykh differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. zametki, 68:4 (2000), 608–619 | DOI | MR | Zbl

[6] N. A. Shananin, “O rasprostranenii invariantnosti rostkov reshenii slabo nelineinykh differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. zametki, 71:1 (2002), 135–143 | DOI | MR | Zbl

[7] N. A. Shananin, “On partial quasi-analyticity of the set of solutions of a set of the Navier–Stokes–type equations”, J. Math. Sci. (New York), 110:2 (2002), 2467–2475 | DOI | MR | Zbl

[8] N. A. Shananin, “O sloevoi strukture mnozhestv simmetriinoi invariantnosti reshenii kvazilineinykh uravnenii”, Matem. zametki, 88:6 (2010), 924–934 | DOI | MR | Zbl

[9] L. Khermander, Analiz lineinykh differentsialrykh operatorov s chastnymi proizvodnymi. T. 3. Psevdodifferentsialnye operatory, Mir, M., 1987 | MR

[10] R. Zulanke, P. Vintgen, Differentsialnaya geometriya i rassloeniya, Mir, M., 1975 | MR | Zbl

[11] R. Narasimkhan, Analiz na deistvitelnykh i kompleksnykh mnogoobraziyakh, Mir, M., 1971 | Zbl

[12] F. Trev, Vvedenie v teoriyu psevdo-differentsialnykh operatorov i integralnykh operatorov Fure, Mir, M., 1984 | MR | Zbl

[13] C. Zuily, Uniqueness and Non-Uniqueness in the Cauchy Problem, Progr. Math., Birkhäuser Boston, Boston, MA, 1983 | MR | Zbl

[14] M. M. Vainberg, Variatsionnye metody issledovaniya nelineinykh operatorov, Gostekhizdat, M., 1956 | Zbl