American Institute of Mathematical Sciences

Advanced
2015, 2015(special): 489-494. doi: 10.3934/proc.2015.0489

Blow-up for nonlinear inequalities with gradient terms and singularities on unbounded sets

Evgeny Galakhov 1, and  Olga Salieva 2,

1. 

Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
2. 

Moscow State Technological University , Vadkovsky lane 3a, Moscow, 127055, Russian Federation

Received  September 2014 Revised  September 2015 Published  November 2015

Nonexistence results for nontrivial solutions for some classes of nonlinear partial differential inequalities with gradient terms and coefficients possessing singularities on unbounded sets are obtained.
Keywords: Nonlinear elliptic inequality, unbounded set, singularity, blow-up, gradient terms..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Evgeny Galakhov, Olga Salieva. Blow-up for nonlinear inequalities with gradient terms and singularities on unbounded sets. Conference Publications, 2015, 2015 (special) : 489-494. doi: 10.3934/proc.2015.0489
References:
[1]

C. Azizieh, P. Clement and E. Mitidieri, Existence and apriori estimates for positive solutions of p-Laplace systems, J. Diff. Eq., 204 (2002), 422-442. Google Scholar

[2]

P. Clement, R. Manasevich and E. Mitidieri, Positive solutions for a quasilinear system via blow-up, Comm. PDE, 18 (1993), 2071-2106. Google Scholar

[3]

A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations, J. Diff. Eq., 250 (2011), 4367-4408. Google Scholar

[4]

A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations II, J. Diff. Eq., 250 (2011), 4409-4436. Google Scholar

[5]

E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, J. Math. Anal. Appl., 408 (2013), 102-113. Google Scholar

[6]

E. Galakhov and O. Salieva, Blow-up for nonlinear inequalities with singularities on unbounded sets,, in, ().   Google Scholar

[7]

E. Mitidieri and S. 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

[8]

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

show all references

References:
[1]

C. Azizieh, P. Clement and E. Mitidieri, Existence and apriori estimates for positive solutions of p-Laplace systems, J. Diff. Eq., 204 (2002), 422-442. Google Scholar

[2]

P. Clement, R. Manasevich and E. Mitidieri, Positive solutions for a quasilinear system via blow-up, Comm. PDE, 18 (1993), 2071-2106. Google Scholar

[3]

A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations, J. Diff. Eq., 250 (2011), 4367-4408. Google Scholar

[4]

A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations II, J. Diff. Eq., 250 (2011), 4409-4436. Google Scholar

[5]

E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, J. Math. Anal. Appl., 408 (2013), 102-113. Google Scholar

[6]

E. Galakhov and O. Salieva, Blow-up for nonlinear inequalities with singularities on unbounded sets,, in, ().   Google Scholar

[7]

E. Mitidieri and S. 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

[8]

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

[1]

Zhijun Zhang. Boundary blow-up for elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights. Communications on Pure & Applied Analysis, 2007, 6 (2) : 521-529. doi: 10.3934/cpaa.2007.6.521
[2]

Marius Ghergu, Vicenţiu Rădulescu. Nonradial blow-up solutions of sublinear elliptic equations with gradient term. Communications on Pure & Applied Analysis, 2004, 3 (3) : 465-474. doi: 10.3934/cpaa.2004.3.465
[3]

Huiling Li, Mingxin Wang. Properties of blow-up solutions to a parabolic system with nonlinear localized terms. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 683-700. doi: 10.3934/dcds.2005.13.683
[4]

Antonio Vitolo, Maria E. Amendola, Giulio Galise. On the uniqueness of blow-up solutions of fully nonlinear elliptic equations. Conference Publications, 2013, 2013 (special) : 771-780. doi: 10.3934/proc.2013.2013.771
[5]

Frédéric Abergel, Jean-Michel Rakotoson. Gradient blow-up in Zygmund spaces for the very weak solution of a linear elliptic equation. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 1809-1818. doi: 10.3934/dcds.2013.33.1809
[6]

Monica Marras, Stella Vernier-Piro, Giuseppe Viglialoro. Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2291-2300. doi: 10.3934/dcdsb.2017096
[7]

Bouthaina Abdelhedi, Hatem Zaag. Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 2607-2623. doi: 10.3934/dcdss.2021032
[8]

José M. Arrieta, Raúl Ferreira, Arturo de Pablo, Julio D. Rossi. Stability of the blow-up time and the blow-up set under perturbations. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 43-61. doi: 10.3934/dcds.2010.26.43
[9]

István Győri, Yukihiko Nakata, Gergely Röst. Unbounded and blow-up solutions for a delay logistic equation with positive feedback. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2845-2854. doi: 10.3934/cpaa.2018134
[10]

Jorge A. Esquivel-Avila. Blow-up in damped abstract nonlinear equations. Electronic Research Archive, 2020, 28 (1) : 347-367. doi: 10.3934/era.2020020
[11]

Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete & Continuous Dynamical Systems, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399
[12]

Yohei Fujishima. Blow-up set for a superlinear heat equation and pointedness of the initial data. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4617-4645. doi: 10.3934/dcds.2014.34.4617
[13]

Shota Sato. Blow-up at space infinity of a solution with a moving singularity for a semilinear parabolic equation. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1225-1237. doi: 10.3934/cpaa.2011.10.1225
[14]

Huyuan Chen, Hichem Hajaiej, Ying Wang. Boundary blow-up solutions to fractional elliptic equations in a measure framework. Discrete & Continuous Dynamical Systems, 2016, 36 (4) : 1881-1903. doi: 10.3934/dcds.2016.36.1881
[15]

Zhifu Xie. General uniqueness results and examples for blow-up solutions of elliptic equations. Conference Publications, 2009, 2009 (Special) : 828-837. doi: 10.3934/proc.2009.2009.828
[16]

Helin Guo, Yimin Zhang, Huansong Zhou. Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1875-1897. doi: 10.3934/cpaa.2018089
[17]

Zhijun Zhang, Ling Mi. Blow-up rates of large solutions for semilinear elliptic equations. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1733-1745. doi: 10.3934/cpaa.2011.10.1733
[18]

Claudia Anedda, Giovanni Porru. Second order estimates for boundary blow-up solutions of elliptic equations. Conference Publications, 2007, 2007 (Special) : 54-63. doi: 10.3934/proc.2007.2007.54
[19]

Jong-Shenq Guo. Blow-up behavior for a quasilinear parabolic equation with nonlinear boundary condition. Discrete & Continuous Dynamical Systems, 2007, 18 (1) : 71-84. doi: 10.3934/dcds.2007.18.71
[20]

Pavol Quittner, Philippe Souplet. Blow-up rate of solutions of parabolic poblems with nonlinear boundary conditions. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 671-681. doi: 10.3934/dcdss.2012.5.671

 Impact Factor: 

Tools

Metrics

  • PDF downloads (40)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy