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 - <p style="white-space: normal; text-align: justify;">The paper proves the nonexistence of the solution for the following Cauchy problem<br/>\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left|\nabla u^{m} \right|^{p-2} \nabla u^{m} \right)-\lambda \; u^{q},&amp;\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), &amp;\qquad x\in {\mathbb{R}}^N,\end{cases}\end{align*}<br/>under some conditions on $m, p, q, \lambda$, where $\delta $ is Dirac function.</p>