The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption
Year: 2021
Author: Qitong Ou
Journal of Partial Differential Equations, Vol. 34 (2021), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v34.n4.4
Journal of Partial Differential Equations, Vol. 34 (2021), Iss. 4 : pp. 369–378
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Non-Newtonian filtration equation Cauchy problem nonexistence.
Author Details
Qitong Ou Email