Criticality for some evolution equations (Q5951374)

The main goal of the paper is to obtain results on critical exponents for equations of the form \[ u_t=(-\Delta)^{\beta/2}u=h(t,x) u^{1+p},\qquad (t,x)\in {\mathbb R}^+\times {\mathbb R}^N \] with given positive initial condition \(u(0,x)=u_0(x)\), \(x\in {\mathbb R}^N\), where \(h(t,x)=O(t^\sigma|x|^\alpha)\) for large \(|x|.\) The results are generalized to the case of a system of two equations of the above form, as well as to hyperbolic-parabolic systems.