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Volume 34, Issue 4
The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption

Qitong Ou

DOI: 10.4208/jpde.v34.n4.4

J. Part. Diff. Eq., 34 (2021), pp. 369-378.

Published online: 2021-08

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  • Abstract

The paper proves the nonexistence of the solution for the following Cauchy problem
\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left|\nabla u^{m} \right|^{p-2} \nabla u^{m} \right)-\lambda \; u^{q},&\qquad \left(x,t\right)\in S_{T} ={\mathbb{R}}^N \times \left(0,T\right), \\u\left(x,\; 0\right)=\delta \left(x\right), &\qquad x\in {\mathbb{R}}^N,\end{cases}\end{align*}
under some conditions on $m, p, q, \lambda$, where $\delta $ is Dirac function.

  • Keywords

Non-Newtonian filtration equation, Cauchy problem, nonexistence.

  • AMS Subject Headings

35B40, 35K65, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ouqitong@xmut.edu.cn (Qitong Ou)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-369, author = {Ou , Qitong}, title = {The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {4}, pages = {369--378}, abstract = {

The paper proves the nonexistence of the solution for the following Cauchy problem
\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left|\nabla u^{m} \right|^{p-2} \nabla u^{m} \right)-\lambda \; u^{q},&\qquad \left(x,t\right)\in S_{T} ={\mathbb{R}}^N \times \left(0,T\right), \\u\left(x,\; 0\right)=\delta \left(x\right), &\qquad x\in {\mathbb{R}}^N,\end{cases}\end{align*}
under some conditions on $m, p, q, \lambda$, where $\delta $ is Dirac function.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/19404.html} }
TY - JOUR T1 - The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption AU - Ou , Qitong JO - Journal of Partial Differential Equations VL - 4 SP - 369 EP - 378 PY - 2021 DA - 2021/08 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/19404.html KW - Non-Newtonian filtration equation, Cauchy problem, nonexistence. AB -

The paper proves the nonexistence of the solution for the following Cauchy problem
\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left|\nabla u^{m} \right|^{p-2} \nabla u^{m} \right)-\lambda \; u^{q},&\qquad \left(x,t\right)\in S_{T} ={\mathbb{R}}^N \times \left(0,T\right), \\u\left(x,\; 0\right)=\delta \left(x\right), &\qquad x\in {\mathbb{R}}^N,\end{cases}\end{align*}
under some conditions on $m, p, q, \lambda$, where $\delta $ is Dirac function.

Qitong Ou. (2021). The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption. Journal of Partial Differential Equations. 34 (4). 369-378. doi:10.4208/jpde.v34.n4.4
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