Geodesic
Wazewski's Method for Nonlinear Evolution Equations
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 705-714.

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

We justify a method for reducing a wide class of nonlinear equations (including several partial differential equations) to ordinary differential equations in locally convex spaces. The possibilities of this method are demonstrated by an example of a class of nonlinear hyperbolic partial differential equations.
Mots-clés : evolution equation
Keywords: hyperbolic partial differential equation, ordinary differential equation, locally convex space, mapping, fixed point, Hadamard differentiability. 
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     title = {Wazewski's {Method} for {Nonlinear} {Evolution} {Equations}},
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S. G. Lobanov. Wazewski's Method for Nonlinear Evolution Equations. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 705-714. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a6/

[1] T. Wazewski, “Sur l'evaluation du domaine d'existence des fonctions implicites réelles ou complexes”, Ann. Soc. Polon. Math., 20 (1947), 81–120 | MR | Zbl

[2] F. Khartman, Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[3] M. Su, “Applications of modified global existence theorems of Cauchy problem”, Nonlinear Stud., 9:3 (2002), 299–306 | MR | Zbl

[4] A. Kaptan, Differentsialnoe ischislenie. Differentsialnye formy, Mir, M., 1971 | MR | Zbl

[5] S. G. Lobanov, “O metode svedeniya nekotorykh klassov nelineinykh uravnenii k evolyutsionnym uravneniyam v lokalno vypuklykh prostranstvakh”, Materialy mezhdunarodnoi konferentsii i Chebyshevskikh chtenii, posvyaschennykh 175-letiyu so dnya rozhdeniya P. L. Chebysheva, t. 2, Izd-vo mekh.-mat. f-ta MGU, M., 1996, 390–393

[6] S. Mizokhata, Teoriya uravnenii s chastnymi proizvodnymi, Mir, M., 1977 | MR | Zbl

[7] S. G. Lobanov, O. G. Smolyanov, “Obyknovennye differentsialnye uravneniya v lokalno vypuklykh prostranstvakh”, UMN, 49:3 (1994), 93–168 | MR | Zbl

[8] J. W. Robbin, “On the existence theorem for differential equations”, Proc. Amer. Math. Soc., 19:4 (1968), 1005–1006 | DOI | MR | Zbl