@Article{CMR-25-4,
author = {Xuesong, Wu and Wenjie, Gao},
title = {Blow-up vs. Global Finiteness for an Evolution $p$-Laplace System with Nonlinear Boundary Conditions},
journal = {Communications in Mathematical Research },
year = {2009},
volume = {25},
number = {4},
pages = {309--317},
abstract = {<p style="text-align: justify;">In this paper, the authors consider the positive solutions of the system of
the evolution $p$-Laplacian equations $$\begin{cases} u_t ={\rm&nbsp;div}(| ∇u |^{p−2} ∇u) + f(u, v), &amp; (x, t) ∈ Ω × (0, T ),
&amp; \\ v_t = {\rm&nbsp;div}(| ∇v |^{p−2} ∇v) + g(u, v), &amp;&nbsp;(x, t) ∈ Ω × (0, T) \end{cases}$$with nonlinear boundary conditions $$\frac{∂u}{∂η}&nbsp;= h(u, v),
\frac{∂v}{∂η} = s(u, v),$$and the initial data $(u_0, v_0)$, where $Ω$ is a bounded domain in&nbsp;$\boldsymbol{R}^n$&nbsp;with smooth
boundary $∂Ω, p &gt; 2$, $h(· , ·)$ and $s(· , ·)$ are positive $C^1$ functions, nondecreasing
in each variable. The authors find conditions on the functions $f, g, h, s$ that prove
the global existence or finite time blow-up of positive solutions for every $(u_0, v_0)$.</p>},
issn = {2707-8523},
doi = {https://doi.org/2009-CMR-19348},
url = {https://global-sci.com/article/81954/blow-up-vs-global-finiteness-for-an-evolution-p-laplace-system-with-nonlinear-boundary-conditions}
}