On blow-up conditions for nonlinear higher order evolution inequalities
Fuente:
arXiv
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| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866929561484132352 |
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| author | Kon'kov, A. A. Shishkov, A. E. |
| author_facet | Kon'kov, A. A. Shishkov, A. E. |
| contents | For the problem $$
\left\{
\begin{aligned}
&
\partial_t^k u
-
\sum_{|α| = m}
\partial^α
a_α(x, t, u)
\ge
f (|u|)
\quad
\mbox{in }
{\mathbb R}_+^{n+1} = {\mathbb R}^n \times (0, \infty),
&
u (x, 0) = u_0 (x),
\:
\partial_t u (x, 0) = u_1 (x),
\ldots,
\partial_t^{k-1} u (x, 0) = u_{k-1} (x) \ge 0,
\end{aligned}
\right. $$ we obtain exact conditions on the function $f$ guaranteeing that any global weak solution is identically zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On blow-up conditions for nonlinear higher order evolution inequalities Kon'kov, A. A. Shishkov, A. E. Analysis of PDEs 35B44, 35B08, 35J30, 35J70 For the problem $$ \left\{ \begin{aligned} & \partial_t^k u - \sum_{|α| = m} \partial^α a_α(x, t, u) \ge f (|u|) \quad \mbox{in } {\mathbb R}_+^{n+1} = {\mathbb R}^n \times (0, \infty), & u (x, 0) = u_0 (x), \: \partial_t u (x, 0) = u_1 (x), \ldots, \partial_t^{k-1} u (x, 0) = u_{k-1} (x) \ge 0, \end{aligned} \right. $$ we obtain exact conditions on the function $f$ guaranteeing that any global weak solution is identically zero. |
| title | On blow-up conditions for nonlinear higher order evolution inequalities |
| topic | Analysis of PDEs 35B44, 35B08, 35J30, 35J70 |
| url | https://arxiv.org/abs/2309.00574 |