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arXiv · 2309.00574

On blow-up conditions for nonlinear higher order evolution inequalities

A. A. Kon'kov·A. E. Shishkov
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Abstract

For the problem $$ \left\{ \begin{aligned} & \partial_t^k u - \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, t, u) \ge f (|u|) \quad \mbox{in } {\mathbb R}_+^{n+1} = {\mathbb R}^n \times (0, \infty), & u (x, 0) = u_0 (x), \: \partial_t u (x, 0) = u_1 (x), \ldots, \partial_t^{k-1} u (x, 0) = u_{k-1} (x) \ge 0, \end{aligned} \right. $$ we obtain exact conditions on the function $f$ guaranteeing that any global weak solution is identically zero.

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A. A. Kon'kov, A. E. Shishkov. 2023-09-01. On blow-up conditions for nonlinear higher order evolution inequalities. https://arxiv.org/abs/2309.00574

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