Geodesic
Blowup of solutions of a Korteweg–de Vries-type equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 64-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the nonlinear third-order differential equation $(u_{xx}-u)_t+u_{xxx}+uu_x=0$ describing the processes in semiconductors with a strong spatial dispersion. We study the problem of the existence of global solutions and obtain sufficient conditions for the absence of global solutions for some initial boundary value problems corresponding to this equation. We consider examples of solution blowup for initial boundary value and Cauchy problems. We use the Mitidieri–Pokhozhaev nonlinear capacity method.
Keywords: initial boundary value problem, solution blowup, global solvability. 
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E. V. Yushkov. Blowup of solutions of a Korteweg–de Vries-type equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 64-72. http://geodesic.mathdoc.fr/item/TMF_2012_172_1_a4/

[1] A. G. Sveshnikov, A. B. Alshin, M. O. Korpusov, Yu. D. Pletner, Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007 | Zbl

[2] S. A. Gabov, Vvedenie v teoriyu nelineinykh voln, Izd-vo MGU, M., 1988 | MR | Zbl

[3] C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, Phys. Rev. Lett., 19:19 (1967), 1095–1097 | DOI | Zbl

[4] S. I. Pokhozhaev, “Ob otsutstvii globalnykh reshenii uravneniya Kortevega–de Friza”, Uravneniya v chastnykh proizvodnykh, Sovremennaya matematika. Fundamentalnye napravleniya, 39, RUDN, M., 2011, 141–150 | MR

[5] S. I. Pokhozhaev, Dokl. RAN, 435:4 (2010), 460–462 | MR

[6] E. Mitidieri, S. I. Pokhozhaev, Tr. MIAN, 234 (2001), 3–383, Nauka, M. | MR | Zbl

[7] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. VIII, Elektrodinamika sploshnykh sred, Nauka, M., 1992 | MR | Zbl

[8] L. E. Elsgolts, Differentsialnye uravneniya i variatsionnoe ischislenie, Nauka, M., 1969 | MR

[9] A. B. Alshin, M. O. Korpusov, E. V. Yushkov, Zh. vychisl. matem. i matem. fiz., 48:5 (2008), 808–812 | DOI | MR | Zbl

[10] J. Lenells, J. Nonlinear Math. Phys., 11:4 (2004), 508–520 | DOI | MR | Zbl