一类具p-Laplace算子和变指数源双曲方程解的爆破  

Blow-Up of Solutions to a Class of Hyperbolic Equations with p-Laplace Operator and Variable Exponential Source

作　　者：吴秀兰[1] 刘立洁[2] 孙鹏[3] WU Xiulan LIU Lijie SUN Peng(College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China Department of Mathematics, Changchun Institute of Education, Changchun 130061, China College of Mathematics, Jilin University, Changchun 130012, China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000 [2]长春教育学院数学系,长春130061 [3]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2017年第5期1177-1180,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金青年基金(批准号:11301211);吉林省教育厅"十三五"科学技术研究项目(批准号:2016211);吉林师范大学博士启动基金(批准号:2014008)

摘　　要：考虑具p-Laplace算子及变指数源双曲方程初边值问题解的爆破性质.利用构造能量泛函方法及凸方法,并结合Sobolev嵌入不等式,证明当1<q^-<q^+≤np-n+p/n-p(p>2),初始能量为正数且初值适当大时,其解在有限时刻爆破.We considered the blow-up properties of solutions of initial boundary value problems to a class of hyperbolic equations with p-Laplace operator and variable exponential source and proved the solutions blow-up in finite time when 1q^-q^＋np-n＋p/n-p（p〉2）,the initial energy was positive and initial value was suitably large with the help of energy functional method,convex method and Sobolev embedding inequalities.

关 键 词：P-LAPLACE算子 双曲方程 正初始能量 爆破 

分 类 号：O175.8[理学—数学]