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May  2017, 16(3): 843-853. doi: 10.3934/cpaa.2017040

On nonexistence of solutions to some nonlinear parabolic inequalities

Olga Salieva

Moscow State Technological Institute "Stankin", Vadkovsky lane 3a, Moscow, 127055, Russia

Received  May 2016 Revised  December 2016 Published  February 2016

Fund Project: The author is supported by RFBR grant 14-01-00736. She also thanks the anonymous referee for her/his helpful comments.

We obtain sufficient conditions for nonexistence of positive solutions to some nonlinear parabolic inequalities with coefficients possessing singularities on unbounded sets.

Keywords: Nonlinear parabolic inequalities, nonexistence, singular coefficients, unbounded sets.
Mathematics Subject Classification: Primary: 35K58, 35K59; Secondary: 35B44.
Citation: Olga Salieva. On nonexistence of solutions to some nonlinear parabolic inequalities. Communications on Pure & Applied Analysis, 2017, 16 (3) : 843-853. doi: 10.3934/cpaa.2017040
References:
[1]

H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. B: Artic. Ric. Mat., 8 (1998), 223-262.   Google Scholar

[2]

E. Galakhov, Some nonexistence results for quasi-linear PDE's, Commun. Pure Appl. Anal., 6 (2007), 141-161.  doi: 10.3934/cpaa.2007.6.141.  Google Scholar

[3]

E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, JMAA, 408 (2013), 102-113.  doi: 10.1016/j.jmaa.2013.05.069.  Google Scholar

[4]

E. Galakhov and O. Salieva, Blow-up of solutions of some nonlinear inequalities with singularities on unbounded sets, Math. Notes, 98 (2015), 222-229.  doi: 10.4213/mzm10622.  Google Scholar

[5]

E. Mitidieri and S. I. Pohozaev, A priori estimates and nonexistence of solutions of nonlinear partial differential equations and inequalities, Proceedings of the Steklov Institute, 234 (2001), 1-383.   Google Scholar

[6]

S. I. Pohozaev, Essentially nonlinear capacities induced by differential operators, Dokl. RAN, 357 (1997), 592-594.   Google Scholar

[7]

G. M. Wei, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, J. Math. Anal. Appl., 28A (2007), 387-394.   Google Scholar

[8]

B. F. Zhong and X. Lijun, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, Journal of Inequalities and Applications, 62 (2014).   Google Scholar

show all references

References:
[1]

H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. B: Artic. Ric. Mat., 8 (1998), 223-262.   Google Scholar

[2]

E. Galakhov, Some nonexistence results for quasi-linear PDE's, Commun. Pure Appl. Anal., 6 (2007), 141-161.  doi: 10.3934/cpaa.2007.6.141.  Google Scholar

[3]

E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, JMAA, 408 (2013), 102-113.  doi: 10.1016/j.jmaa.2013.05.069.  Google Scholar

[4]

E. Galakhov and O. Salieva, Blow-up of solutions of some nonlinear inequalities with singularities on unbounded sets, Math. Notes, 98 (2015), 222-229.  doi: 10.4213/mzm10622.  Google Scholar

[5]

E. Mitidieri and S. I. Pohozaev, A priori estimates and nonexistence of solutions of nonlinear partial differential equations and inequalities, Proceedings of the Steklov Institute, 234 (2001), 1-383.   Google Scholar

[6]

S. I. Pohozaev, Essentially nonlinear capacities induced by differential operators, Dokl. RAN, 357 (1997), 592-594.   Google Scholar

[7]

G. M. Wei, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, J. Math. Anal. Appl., 28A (2007), 387-394.   Google Scholar

[8]

B. F. Zhong and X. Lijun, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, Journal of Inequalities and Applications, 62 (2014).   Google Scholar

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