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Volume 35, Issue 3
Asymptotic Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-Type Sources

Yingzhen Xue

DOI: 10.4208/jpde.v35.n3.4

J. Part. Diff. Eq., 35 (2022), pp. 240-258.

Published online: 2022-06

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  • Abstract

In the paper, the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied. By constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem, the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained. The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundary conditions.

  • Keywords

Porous media equations, norm-type sources, the global existence, the finite time blow-up, the blow up time.

  • AMS Subject Headings

35K20, 35K55, 35K60, 35K65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xueyingzhen@126.com (Yingzhen Xue)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-35-240, author = {Xue , Yingzhen}, title = {Asymptotic Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-Type Sources}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {3}, pages = {240--258}, abstract = {

In the paper, the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied. By constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem, the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained. The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundary conditions.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/20774.html} }
TY - JOUR T1 - Asymptotic Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-Type Sources AU - Xue , Yingzhen JO - Journal of Partial Differential Equations VL - 3 SP - 240 EP - 258 PY - 2022 DA - 2022/06 SN - 35 DO - http://doi.org/10.4208/jpde.v35.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/20774.html KW - Porous media equations, norm-type sources, the global existence, the finite time blow-up, the blow up time. AB -

In the paper, the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied. By constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem, the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained. The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundary conditions.

Xue , Yingzhen. (2022). Asymptotic Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-Type Sources. Journal of Partial Differential Equations. 35 (3). 240-258. doi:10.4208/jpde.v35.n3.4
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