Comptes Rendus
Articles du volume en cours
Note
A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up
Qigang Deng1  ; Fugeng Zeng1   ; Min Jiang1 
1 School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, PR China
Comptes Rendus. Mécanique, Volume 350 (2022), pp. 269-282.

In this paper, we study the initial-boundary value problem of the singular non-Newton filtration equation with logarithmic nonlinearity. By using the concavity method, we obtain the existence of finite time blow-up solutions at initial energy J(u 0 )⩽d. Furthermore, we discuss the asymptotic behavior of the weak solution and prove that the weak solution converges to the corresponding stationary solution as t→+∞. Finally, we give sufficient conditions for global existence and blow-up of solutions at initial energy J(u 0 )>d.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmeca.117
Mots clés : Non-Newton filtration equation, Singular potential, Global existence, Blow-up, Logarithmic nonlinearity
Qigang Deng 1 ; Fugeng Zeng 1 ; Min Jiang 1

1 School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, PR China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMECA_2022__350_G2_269_0,
     author = {Qigang Deng and Fugeng Zeng and Min Jiang},
     title = {A singular {non-Newton} filtration equation with logarithmic nonlinearity: global existence and blow-up},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {269--282},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {350},
     year = {2022},
     doi = {10.5802/crmeca.117},
     zbl = {07509990},
     language = {en},
}
TY  - JOUR
AU  - Qigang Deng
AU  - Fugeng Zeng
AU  - Min Jiang
TI  - A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up
JO  - Comptes Rendus. Mécanique
PY  - 2022
SP  - 269
EP  - 282
VL  - 350
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.117
LA  - en
ID  - CRMECA_2022__350_G2_269_0
ER  - 
%0 Journal Article
%A Qigang Deng
%A Fugeng Zeng
%A Min Jiang
%T A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up
%J Comptes Rendus. Mécanique
%D 2022
%P 269-282
%V 350
%I Académie des sciences, Paris
%R 10.5802/crmeca.117
%G en
%F CRMECA_2022__350_G2_269_0
Qigang Deng; Fugeng Zeng; Min Jiang. A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 269-282. doi : 10.5802/crmeca.117. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.117/

[1] Z. Q. Wu; J. N. Zhao; J. X. Yin; H. L. Li Nonlinear Diffusion Equations, World Scientific Publishing Company, Singapore, 2001

[2] Z. Tan Non-Newton filtration equation with special medium void, Acta Math. Sci., Volume 24 (2004) no. 1, pp. 118-128 | DOI | MR | Zbl

[3] Y. Wang The existence of global solution and the blowup problem for some p-Laplace heat equations, Acta Math. Sci., Volume 27 (2007) no. 2, pp. 274-282 | DOI | MR

[4] J. Zhou A multi-dimension blow-up problem to a porous medium diffusion equation with special medium void, Appl. Math. Lett., Volume 30 (2014), pp. 6-11 | DOI | MR | Zbl

[5] J. Zhou Global existence and blow-up of solutions for a non-newton polytropic filtration system with special volumetric moisture content, Comput. Math. Appl., Volume 71 (2016) no. 5, pp. 1163-1172 | DOI | MR | Zbl

[6] G. Y. Xu; J. Zhou Global existence and blow-up of solutions to a singular non-Newton polytropic filtration equation with critical and supercritical initial energy, Commun. Pure Appl. Anal., Volume 17 (2018) no. 5, pp. 1805-1820 | MR | Zbl

[7] W. Lian; J. Wang; R. Z. Xu Global existence and blow up of solutions for pseudo-parabolic equation with singular potential, J. Differ. Equ., Volume 269 (2020) no. 6, pp. 4914-4959 | DOI | MR

[8] M. Feng; J. Zhou Global existence and blow-up of solutions to a nonlocal parabolic equation with singular potential, J. Math. Anal. Appl., Volume 464 (2018) no. 2, pp. 1213-1242 | DOI | MR | Zbl

[9] X. M. Deng; J. Zhou Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity, Commun. Pure Appl. Anal., Volume 19 (2020) no. 2, pp. 923-939 | DOI | MR | Zbl

[10] L. Gross Logarithmic sobolev inequalities, Am. J. Math., Volume 97 (1975) no. 4, pp. 1061-1083 | DOI | MR

[11] G. Duong; V. Nguyen; H. Zaag Construction of a stable blowup solution with a prescribed behavior for a non-scaling-invariant semilinear heat equation, Tunis. J. Math., Volume 1 (2019) no. 1, pp. 13-45 | DOI | MR | Zbl

[12] M. A. Hamza; H. Zaag The blow-up rate for a non-scaling invariant semilinear heat equation, Arch. Rat. Mech. Anal., Volume 244 (2022) no. 1, pp. 87-125 | DOI | MR | Zbl

[13] P. Souplet Universal estimates and Liouville theorems for superlinear problems without scale invariance, 2022 (preprint) | arXiv

[14] M. L. Liao; Z. Tan Global existence and blow-up of solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity, 2020 (preprint) | arXiv

[15] O. A. Ladyzhenskaia; V. A. Solonnikov; N. N. Uraltseva Linear and Quasi-Linear Equations of Parabolic Type, American Mathematical Society, Providence, 1988

[16] Y. J. He; H. H. Gao; H. Wang Blow-up and decay for a class of pseudo-parabolic p-Laplacian equation with logarithmic nonlinearity, Comput. Math. Appl., Volume 75 (2018) no. 2, pp. 459-469 | DOI | MR | Zbl

[17] H. A. Levine Instability and nonexistence of global solutions to nonlinear wave equations of the form Pu tt = -Au + F(u), Trans. Am. Math. Soc., Volume 192 (1974), pp. 1-21 | MR

Cité par Sources :

Commentaires - Politique