@article{SM_2013_204_3_a1,
author = {M. O. Korpusov},
title = {Solution blow-up for a~class of parabolic equations with double nonlinearity},
journal = {Sbornik. Mathematics},
pages = {323--346},
year = {2013},
volume = {204},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2013_204_3_a1/}
}
M. O. Korpusov. Solution blow-up for a class of parabolic equations with double nonlinearity. Sbornik. Mathematics, Tome 204 (2013) no. 3, pp. 323-346. http://geodesic.mathdoc.fr/item/SM_2013_204_3_a1/
[1] A. S. Kalashnikov, “Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations”, Russian Math. Surveys, 42:2 (1987), 169–222 | DOI | MR | Zbl
[2] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, de Gruyter, Paris, 1969 | MR | MR | Zbl | Zbl
[3] P. A. Raviart, “Sur la résolution de certaines équations paraboliques non linéaires”, J. Functional Analysis, 5:2 (1970), 299–328 | DOI | MR | Zbl
[4] A. V. Ivanov, “Quasilinear parabolic equations admitting double degeneracy”, St. Petersburg Math. J., 4:6 (1993), 1153–1168 | MR | Zbl
[5] G. I. Laptev, “Weak solutions of second-order quasilinear parabolic equations with double non-linearity”, Sb. Math., 188:9 (1997), 1343–1370 | DOI | DOI | MR | Zbl
[6] G. I. Laptev, “Evolution equations with monotone operator and functional non-linearity at the time derivative”, Sb. Math., 191:9 (2000), 1301–1322 | DOI | DOI | MR | Zbl
[7] H. A. Levine, S. R. Park, J. Serrin, “Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type”, J. Differential Equations, 142:1 (1998), 212–229 | DOI | MR | Zbl
[8] E. Mitidieri, S. I. Pohozaev, “A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities”, Proc. Steklov Inst. Math., 234 (2001), 1–362 | MR | Zbl | Zbl
[9] A. B. Al'shin, M. O. Korpusov, A. G. Sveshnikov, Blow-up in nonlinear Sobolev type equations, De Gruyter Ser. Nonlinear Anal. Appl., 15, de Gruyter, Berlin, 2011 | MR | Zbl
[10] H. A. Levine, “Instability and nonexistence of global solutions to nonlinear wave equations of the form $Pu_{tt}=-Au+\mathscr{F}(u)$”, Trans. Amer. Math. Soc., 192 (1974), 1–21 | DOI | MR | Zbl
[11] V. K. Kalantarov, O. A. Ladyzhenskaya, “The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types”, J. Soviet Math., 10:1 (1978), 53–70 | DOI | MR | Zbl | Zbl
[12] V. P. Demidovich, Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR | Zbl
[13] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'tseva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, RI, 1968 | MR | MR | Zbl | Zbl