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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We give sufficient conditions for global (and local) existence of positive mild solutions for the weak coupled system \begin{eqnarray*} \frac{\partial u_{1}}{\partial t} &=&\rho _{1}t^{\rho _{1}-1}\Delta _{\alpha _{1}}u_{1}+t^{\sigma _{1}}u_{2}^{\beta _{1}},\text{\ \ }u_{1}\left( 0\right) =\varphi _{1}, \\ \frac{\partial u_{2}}{\partial t} &=&\rho _{2}t^{\rho _{2}-1}\Delta _{\alpha _{2}}u_{2}+t^{\sigma _{2}}u_{1}^{\beta _{2}},\text{\ \ }u_{2}\left( 0\right) =\varphi _{2}, \end{eqnarray*}% where $\Delta _{\alpha _{i}}$ is a fractional Laplacian, $0 0,\ \sigma _{i}>-1\ $are constants and the initial data $\varphi _{i}$ are positive, bounded and integrable functions.

Existence of mild solutions for a system of partial differential equations with time-dependent generators