Geodesic
On blow-up of solutions of some systems of quasilinear parabolic inequalities
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 84-92.

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We study systems of parabolic inequalities (including singular and degenerate ones), which contain squares of first derivatives of the unknown function with respect to spatial variables. We establish conditions that guarantee nonexistence of their global solutions. 
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A. B. Muravnik. On blow-up of solutions of some systems of quasilinear parabolic inequalities. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 84-92. http://geodesic.mathdoc.fr/item/CMFD_2013_48_a6/

[1] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR | Zbl

[2] Denisov V. N., Muravnik A. B., “O stabilizatsii resheniya zadachi Koshi dlya kvazilineinykh parabolicheskikh uravnenii”, Diff. uravn., 38:3 (2002), 351–355 | MR | Zbl

[3] Mitidieri E., Pokhozhaev S. I., “Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh”, Tr. MIAN, 234, 2001, 3–383 | MR | Zbl

[4] Burgan J. R., Munier A., Feix M. R., Fijalkow E., “Homology and the nonlinear heat diffusion equation”, SIAM J. Appl. Math., 44 (1984), 11–18 | DOI | MR | Zbl

[5] Caristi G., “Existence and nonexistence of global solutions of degenerate and singular parabolic systems”, Abstr. Appl. Anal., 5:4 (2000), 265–284 | DOI | MR

[6] Kardar M., Parisi G., Zhang Y.-C., “Dynamic scaling of growing interfaces”, Phys. Rev. Lett., 56 (1986), 889–892 | DOI | Zbl

[7] Medina E., Hwa T., Kardar M., Zhang Y.-C., “Burgers equation with correlated noise: renormalization group analysis and applications to directed polymers and interface growth”, Phys. Rev. A, 39 (1989), 3053–3075 | DOI | MR