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arXiv · 1803.06757

On stabilization of solutions of higher order evolution inequalities

A. A. Kon'kov·A. E. Shishkov
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Abstract

We obtain sharp conditions guaranteeing that every non-negative weak solution of the inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, t, u) - u_t \ge f (x, t) g (u) \quad \mbox{in} {\mathbb R}_+^{n+1} = {\mathbb R}^n \times (0, \infty), \quad m,n \ge 1, $$ stabilizes to zero as $t \to \infty$. These conditions generalize the well-known Keller-Osserman condition on the grows of the function $g$ at infinity.

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A. A. Kon'kov, A. E. Shishkov. 2018-03-18. On stabilization of solutions of higher order evolution inequalities. https://arxiv.org/abs/1803.06757

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