Absence of local and global solutions to weakly coupled systems of parabolic inequalities (Q1420687)

The goal of this paper is to discuss the nonexistence of weak solutions to systems of parabolic inequalities with a fractional power of the Laplacian \((-\Delta)^{\alpha/2}\), \(0<\alpha\leq 2\), namely \[ \begin{cases} u_t\geq- (-\Delta)^{\beta/2} u+h_1(x,t)| v|^p\\ v_t\geq-(-\Delta)^{\alpha/2} v+h_2(x,t)| u|^q,\end{cases} \tag{1} \] where \(S_T:= \mathbb{R}^N \times(0,T)\), \(0<T\leq+\infty\), and \(0<\alpha,\beta\leq 2\), \(p>1\), \(q>1\). The results of the author include nonexistence results as well as necessary conditions for the local and global solvability of (1).