English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we investigate the nonexistence of nonnegative solutions ofparabolic inequalities of the form $$\begin{cases} &u_t \pm L_\mathcal A u\geq(K\ast u^p)u^q \quad\mbox{ in } \mathbb R^N \times \mathbb (0,\infty),\, N\geq1,\\ &u(x,0) = u_0(x)\ge0 \,\, \text{ in } \mathbb R^N,\end{cases} \qquad(P^{\pm}) $$ where $u_0\in L^1_{loc}({\mathbb R}^N)$, $L_{\mathcal{A}}$ denotesa weakly $m$-coercive operator, which includes as prototype the $m$-Laplacianor the generalized mean curvature operator, $p,\,q>0$, while $K\ast u^p$ standsfor the standard convolution operator between a weight $K>0$ satisfyingsuitable conditions at infinity and $u^p$. For problem $(P^-)$ we obtain aFujita type exponent while for $(P^+)$ we show that no such critical exponentexists. Our approach relies on nonlinear capacity estimates adapted to thenonlocal setting of our problems. No comparison results or maximum principlesare required.

Fujita type results for quasilinear parabolic inequalities with nonlocal terms