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May
2017, 16(3): 843-853.
doi: 10.3934/cpaa.2017040
On nonexistence of solutions to some nonlinear parabolic inequalities
Moscow State Technological Institute "Stankin", Vadkovsky lane 3a, Moscow, 127055, Russia |
We obtain sufficient conditions for nonexistence of positive solutions to some nonlinear parabolic inequalities with coefficients possessing singularities on 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 and Applied Analysis,
2017, 16
(3)
: 843-853.
doi: 10.3934/cpaa.2017040
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References:
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H. Brezis and X. Cabré,
Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. B: Artic. Ric. Mat., 8 (1998), 223-262.
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| [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. |
| [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. |
| [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. |
| [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.
|
| [6] |
S. I. Pohozaev,
Essentially nonlinear capacities induced by differential operators, Dokl. RAN, 357 (1997), 592-594.
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G. M. Wei,
Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, J. Math. Anal. Appl., 28A (2007), 387-394.
|
| [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).
|
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.
|
| [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. |
| [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. |
| [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. |
| [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.
|
| [6] |
S. I. Pohozaev,
Essentially nonlinear capacities induced by differential operators, Dokl. RAN, 357 (1997), 592-594.
|
| [7] |
G. M. Wei,
Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, J. Math. Anal. Appl., 28A (2007), 387-394.
|
| [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).
|
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