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 . Furthermore, we discuss the asymptotic behavior of the weak solution and prove that the weak solution converges to the corresponding stationary solution as . Finally, we give sufficient conditions for global existence and blow-up of solutions at initial energy .
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DOI : 10.5802/crmeca.117
Qigang Deng 1 ; Fugeng Zeng 1 ; Min Jiang 1
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@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/
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