On large time behavior of solutions of higher order evolution inequalities with fast diffusion

We obtain stabilization conditions and large time estimates for weak solutions of the inequality ∑|α|=m∂αaα(x,t,u)−ut≥f(x,t)g(u)in Ω×(0,∞), where Ω is a non-empty open subset of Rn, m,n≥1, and aα are Caratheodory functions such that |aα(x,t,ζ)|≤Aζp,|α|=m, with some constants A>0 and 0<p<1 for almost all (x,t)∈Ω×(0,∞) and for all ζ∈[0,∞). For solutions of homogeneous differential inequalities, we give an exact universal upper bound. © 2021 Elsevier Inc.