The space structure near a blow-up point for semilinear heat equations: A formal approach
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 31 (1991) no. 3, pp. 399-411 Cet article a éte moissonné depuis la source Math-Net.Ru

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     title = {The space structure near a blow-up point for semilinear heat equations: {A~formal} approach},
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J. J. L. Velázquez; V. A. Galaktionov; M. A. Herrero. The space structure near a blow-up point for semilinear heat equations: A formal approach. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 31 (1991) no. 3, pp. 399-411. http://geodesic.mathdoc.fr/item/ZVMMF_1991_31_3_a6/

[1] Galaktionov V. A., Posashkov S. A., Uravnenie $u_t=u_{xx}+u^\beta$. Lokalizatsiya, asimptoticheskoe povedenie neogranichennykh reshenii, Preprint No 97, IPMatem. AN SSSR, M., 1985

[2] Giga Y., Kohn R. V., “Asymptotic self-similar blow-up of semilinear heat equations”, Communs Pure and Appl. Math., 38 (1985), 297–319 | DOI | MR | Zbl

[3] Galaktionov V. A., Posashkov S. A., “Primenenie novykh teorem sravneniya k issledovaniyu neogranichennykh reshenii nelineinykh parabolicheskikh uravnenii”, Differents. ur-niya, 22:7 (1986), 1165–1173 | MR | Zbl

[4] Giga Y., Kohn R. V., “Characterizing blow-up using similarity variables”, Indiana Univ. Math. J., 36 (1987), 1–40 | DOI | MR | Zbl

[5] Galaktionov V. A., Posashkov S. A., “Modelirovanie protsessov obostreniya v zadachakh teploprovodnosti s nelineinym istochnikom”, Matem. modelirovanie, 1:12 (1989), 89–108 | MR | Zbl

[6] Giga Y., Kohn R. V., “Nondegeneracy of blow-up points for semilinear heat equations”, Communs Pure and Appl. Math., 42 (1989), 845–884 | DOI | MR | Zbl

[7] Bebernes J., Bressan A., Eberly D., “A description of blow-up for the solid fuel ignition model”, Indiana Univ. Math. J., 36 (1987), 295–305 | DOI | MR

[8] Bressan A., On the asymptotic shape of blow-up (to appear)

[9] Liu W., “The blow-up rate of solutions of semilinear heat equations”, J. Different. Equat., 77 (1989), 104–122 | DOI | MR | Zbl

[10] Hocking L. M., Stewartson K., Stuart J. T., “A non-linear instability burst in plane parallel flow”, J. Fluid Mech., 51 (1972), 705–735 | DOI | Zbl

[11] Dold J. W., “Analysis of the early stage of thermal runaway”, Quart. J. Mech. ami Appl. Math., 38 (1985), 361–387 | DOI | Zbl

[12] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | MR

[13] Berger M., Kohn R. V., “A rescaling algorithm for the numerical calculation of blowing up solutions”, Communs Pure and Appl. Math., 41 (1988), 841–863 | DOI | MR | Zbl

[14] Bebernes J., Bressan A., Lacey A. A., “Total blow-up versus single point blow-up”, J. Different. Equat., 73 (1988), 30–44 | DOI | MR | Zbl

[15] Samarskii A. A., Elenin G. G., Zmitrenko N. V. i dr., “Gorenie nelineinoi sredy v vide slozhnykh struktur”, Dokl. AN SSSR, 237:6 (1977), 1330–1333 | MR

[16] Elenin G. G., Kurdyumov S. P., Samarskii A. A., “Nestatsionarnye dissipativnye struktury v nelineinoi teploprovodnoi srede”, Zh. vychisl. matem. i matem. fiz., 23:2 (1983), 380–390 | MR | Zbl

[17] Galaktionov V. A., Kurdyumov S. P., Posashkov S. A., Samarskii A. A., “Kvazilineinoe parabolicheskoe uravnenie so slozhnym spektrom neogranichennykh avtomodelnykh reshenii”, Matem. modelirovanie. Protsessy v nelineinykh sredakh, Nauka, M., 1986, 142–182 | MR

[18] Gaiaktionov V. A., Herrero M. A., Velázquez J. J. L., The structure of solutions near an extinction point in semilinear heat equations with strong absorption: a formal approach (to appear)