Volume 53, Issue 3
On the Generalized Porous Medium Equation in Fourier-Besov Spaces

Weiliang Xiao & Xuhuan Zhou

J. Math. Study, 53 (2020), pp. 316-328.

Published online: 2020-05

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  • Abstract

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.

  • AMS Subject Headings

42B37, 76S05, 35Q35, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xwltc123@163.com (Weiliang Xiao)

zhouxuhuan@163.com (Xuhuan Zhou)

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@Article{JMS-53-316, author = {Xiao , Weiliang and Zhou , Xuhuan}, title = {On the Generalized Porous Medium Equation in Fourier-Besov Spaces}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {3}, pages = {316--328}, abstract = {

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n3.20.05}, url = {http://global-sci.org/intro/article_detail/jms/16922.html} }
TY - JOUR T1 - On the Generalized Porous Medium Equation in Fourier-Besov Spaces AU - Xiao , Weiliang AU - Zhou , Xuhuan JO - Journal of Mathematical Study VL - 3 SP - 316 EP - 328 PY - 2020 DA - 2020/05 SN - 53 DO - http://doi.org/10.4208/jms.v53n3.20.05 UR - https://global-sci.org/intro/article_detail/jms/16922.html KW - Porous medium equation, well-posedness, blowup criterion, Fourier-Besov spaces. AB -

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.

Xiao , Weiliang and Zhou , Xuhuan. (2020). On the Generalized Porous Medium Equation in Fourier-Besov Spaces. Journal of Mathematical Study. 53 (3). 316-328. doi:10.4208/jms.v53n3.20.05
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