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- W2953231300 abstract "In this paper we study classical solutions to the zero--flux attraction--repulsion chemotaxis--system begin{equation}label{ProblemAbstract} tag{$Diamond$} begin{cases} u_{ t}=Delta u -chi nabla cdot (unabla v)+xi nabla cdot (unabla w) & textrm{in }Omegatimes 0=Delta v+alpha u-beta v & textrm{in } Omegatimes (0,t^*), 0=Delta w+gamma u-delta w & textrm{in } Omegatimes (0,t^*), end{cases} end{equation} where $Omega$ is a smooth and bounded domain of $mathbb{R}^2$, $t^*$ is the blow--up time and $alpha,beta,gamma,delta,chi,xi$ are positive real numbers. From the literature it is known that under a proper interplay between the above parameters and suitable smallness assumptions on the initial data $u({bf x},0)=u_0in C^0(bar{Omega})$, system eqref{ProblemAbstract} has a unique classical solution which becomes unbounded as $tnearrow t^*$. The main result of this investigation is to provide an explicit lower bound for $t^*$ estimated in terms of $int_Omega u_0^2 d{bf x}$ and attained by means of well--established techniques based on ordinary differential inequalities." @default.
- W2953231300 created "2019-06-27" @default.
- W2953231300 creator A5028943838 @default.
- W2953231300 date "2019-03-19" @default.
- W2953231300 modified "2023-09-27" @default.
- W2953231300 title "Explicit lower bound of blow--up time for an attraction--repulsion chemotaxis system" @default.
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