The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption (Journal of Partial Differential Equations, 2021)
The paper proves the nonexistence of the solution for the following Cauchy problem\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left| abla u^{m} \right|^{p-2} abla 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.