具有弱、强阻尼项和对数非线性的$p$- laplace双曲型方程解的全局适定性

Pub Date : 2022-01-01 DOI:10.11650/tjm/220702

N. Boumaza, Billel Gheraibia, Gongwei Liu

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引用次数: 4

摘要

本文研究了具有弱阻尼项和强阻尼项以及对数非线性的p-拉普拉斯双曲型方程。利用势阱方法和对数Sobolev不等式，我们证明了在两种情况E（0）0（ω=0）问题解的有限时间爆破。

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Global Well-posedness of Solutions for the $p$-Laplacian Hyperbolic Type Equation with Weak and Strong Damping Terms and Logarithmic Nonlinearity

. In this paper, we consider the p -Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we prove global existence, inﬁnite time blow up and asymptotic behavior of solutions in two cases E (0) < d and E (0) = d . Furthermore, the inﬁnite time blow up of solutions for the problem with E (0) > 0 ( ω = 0) is studied.

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