On blow-up conditions for nonlinear higher order evolution inequalities

2023/09/01 by A. A. Kon’kov, Andrey Shishkov, Kon'kov, A. A. +1
Mathematics · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2309.00574

Abstract

For the problem \ \beginaligned amp; ∂_t^k u - ∑_{|α| = m} ∂^α a_α(x, t, u) ≥ f (|u|) in \mathbb R₊ⁿ⁺¹ = \mathbb Rⁿ × (0, ∞), amp; u (x, 0) = u₀ (x), ∂_t u (x, 0) = u₁ (x), …, ∂_t^k-1 u (x, 0) = u_k-1 (x) ≥ 0, \endaligned . we obtain exact conditions on the function f guaranteeing that any global weak solution is identically zero.

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