2020/11/01 by A. A. Kon’kov, Andrey Shishkov, Kon'kov, A. A. +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2011.00599
We obtain stabilization conditions and large time estimates for weak solutions of the inequality ∑|α| = m ∂α aα(x, t, u) - ut ≥ f (x, t) g (u) in Ω× (0, ∞), where Ω is a non-empty open subset of \mathbb Rn, m, n ≥ 1, and aα are Caratheodory functions such that |aα(x, t, ζ)| ≤ A ζp, |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.