The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption

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