Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions
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摘要: 考虑在动态边界条件下, 非线性~$p$($x$)-Kirchhoff~方程组解的非全局存在性, 该方程组带有非线性外力项~$Q$~和非线性源项$~f$. 通过研究方程组解的自然能量, 证明在初始能量小于一个临界值时, 方程组解的非全局存在性. 并将带有拟线性齐次~$p$-拉普拉斯算子的~$p$-Kirchhoff~方程组推广到~$p(x)$-Kirchhoff~方程组, 该方程组近年被用来模拟很多现象.
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关键词:
- p(x)$-Kirchhoff~方程组 /
- 非全局存在性 /
- 非线性源项和外力项
Abstract: This paper considered the global non-existence of solutions of nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions, which involve nonlinear external damping terms $Q$ and nonlinear driving forces $f$. Through the study of the natural energy associated to the solutions $u$ of the systems, the nonexistence of global solutions, when the initial energy is controlled above by a critical value was proved. And the $p$-Kirchhoff equations involving the quasilinear homogeneous $p$-Laplace operator were extended to the $p(x)$-Kirchhoff equations which have been used in the last decades to model various phenomena. -
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