具有超线性源的拟线性双曲型方程爆破时间的下界估计

IF 1 4区工程技术 Q4 MECHANICS

Comptes Rendus Mecanique Pub Date : 2020-10-06 DOI:10.5802/crmeca.9

G. Zu, Fang-lan Li

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引用次数: 0

摘要

研究一类强阻尼拟线性双曲型方程爆破解的下界。采用带修正常数的逆Hölder不等式克服了嵌入不等式失效所带来的困难。此外，通过构造一个新的具有小耗散项的控制泛函，并应用一个逆Hölder不等式和能量不等式，得到了爆破时间的下界。该结果对[1]中提出的开放问题给出了一个肯定的答案。

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Lower bound estimates of blow-up time for a quasilinear hyperbolic equation with superlinear sources

This paper deals with the lower bound for blow-up solutions to a quasilinear hyperbolic equation with strong damping. An inverse Hölder inequality with a correction constant is employed to overcome the difficulty caused by the failure of the embedding inequality. Moreover, a lower bound for blow-up time is obtained by constructing a new control functional with a small dissipative term and by applying an inverse Hölder inequality as well as energy inequalities. This result gives a positive answer to the open problem presented in [1].

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来源期刊

Comptes Rendus Mecanique 物理-力学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The Comptes rendus - Mécanique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … The journal publishes original and high-quality research articles. These can be in either in English or in French, with an abstract in both languages. An abridged version of the main text in the second language may also be included.