一类随时间非线性抛物型Kirchhoff方程解的寿命

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2020-01-01 DOI:10.3934/eect.2020088

Haixia Li

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引用次数: 1

摘要

研究了一类具有时相关非线性的抛物型Kirchhoff方程的初边值问题。给出了一种新的非负初始能量爆破准则，并推导了爆破时间的上界和下界。这些结果部分推广了Han和Li在[具有任意初始能量的Kirchhoff方程整体解和爆破解的存在性的阈值结果，计算机与数学应用，75(2018)，3283-3297]中最近得到的一些结果。

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Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity

In this paper, an initial boundary value problem for a parabolic type Kirchhoff equation with time-dependent nonlinearity is considered. A new blow-up criterion for nonnegative initial energy is given and upper and lower bounds for the blow-up time are also derived. These results partially generalize some recent ones obtained by Han and Li in [Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75(2018), 3283-3297].

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology