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

作　　者：明森 郝江浩[2] 杜嘉仪 MING Sen;HAO Jianghao;DU Jiayi(Department of Mathematics,North University of China,Taiyuan 030051,China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]中北大学数学学院,太原030051 [2]山西大学数学科学学院,太原030006

出　　处：《数学年刊（A辑）》2024年第1期71-96,共26页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11871315);山西省自然科学基金(No.201901D211276);山西省基础研究计划(No.20210302123045,No.20210302123182)的资助。

摘　　要：本文研究Schwarzschild时空中非线性波动方程耦合方程组的Cauchy问题解的破裂性态.问题的非线性项包含混合型记忆项、组合和幂次型记忆项、组合和导数型记忆项以及组合型记忆项.当非线性项的指数满足一定假设时,利用迭代方法建立解的生命跨度的上界估计.创新之处是在Schwarzschild度量下分析非线性记忆项对解的生命跨度估计的影响.据已有文献所知,定理1.1-1.4中的结果是新的.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.

关 键 词：耦合方程组 记忆项 迭代方法 破裂 生命跨度估计 

分 类 号：O177.92[理学—数学]