Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions

LI Xi-liu; MU Chun-lai; ZENG Rong; ZHOU Shou-ming

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Jul. 2013

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Article Navigation > Journal of East China Normal University (Natural Sciences) > 2013 > (3): 149-163，175

LI Xi-liu, MU Chun-lai, ZENG Rong, ZHOU Shou-ming. Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions[J]. Journal of East China Normal University (Natural Sciences), 2013, (3): 149-163，175.

Citation:

LI Xi-liu, MU Chun-lai, ZENG Rong, ZHOU Shou-ming. Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions[J]. Journal of East China Normal University (Natural Sciences), 2013, (3): 149-163，175.

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Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions

1.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
2.
School of Economic Mathematics, Southwestern

Received Date: 2012-04-01
Rev Recd Date: 2012-07-01
Publish Date: 2013-05-25

Abstract

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.
- $p(x)$-Kirchhoff systems,
- global non-existence,
- nonlinear source and boundary damping terms

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References(1)

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