明森,郝江浩,杜嘉仪.Schwarzschild时空中带记忆项的波动方程耦合方程组解的奇性[J].数学年刊A辑,2024,(1):71~96
Schwarzschild时空中带记忆项的波动方程耦合方程组解的奇性
Formation of Singularities of Solutions to the Coupled System of Wave Equations with Memory Terms in Schwarzschild Spacetime
投稿时间:2022-06-23  修订日期:2023-11-14
DOI:10.16205/j.cnki.cama.2024.0007
中文关键词:  kurzweil积分  Lyapunov泛函  饱和解  一致有界
英文关键词:Coupled system  Memory terms  Iteration method  Blow-up  Lifespan estimates
基金项目:国家自然科学基金(No.12161080)
作者单位
明森 通信作者. 中北大学数学学院, 太原 030051. 
郝江浩 山西大学数学科学学院, 太原 030006. 
杜嘉仪 中北大学数学学院, 太原 030051. 
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中文摘要:
      本文通过建立滞后型脉冲泛函微分方程饱和解的存在唯一性定理,在广义常微分方程与滞后型脉冲泛函微分方程等价的基础上,研究了滞后型脉冲泛函微分方程关于一致有界性的Lyapunov逆定理.
英文摘要:
      The main purpose of this work is to consider blow-up dynamics of solutions to the Cauchy problem for coupled system of nonlinear wave equations in Schwarzschild spacetime. The nonlinear terms in the problem include mixed type memory terms, combined and power type memory terms, combined and derivative type memory terms as well as combined type memory terms. Furthermore, upper bound lifespan estimates of solutions are established by imposing certain assumptions on the exponents in the nonlinear terms and making use of the iteration method. The main novelty is that that authors analyze the effects of nonlinear memory terms on lifespan estimates of solutions under the Schwarzschild metric. To the best of the authors’ knowledge, the results in Theorems 1.1–1.4 are new
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