一类具超临界源非线性双曲方程解的爆破时间下界估计
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摘要
通过构造具小耗散项的新控制泛函,利用能量估计不等式和反向H?lder不等式,对一类具超临界源项的非线性双曲方程解的L~p范数建立一阶非线性微分不等式,并通过讨论微分不等式的性质获得解爆破时间的精确下界估计.
By constructing a new control function with small dissipative term,using energy estimate inequalities and inverse H?lder inequality,the first order nonlinear differential inequality was established about the L~p norm of the solutions of a class of nonlinear hyperbolic equations with supercritical source terms,and the accurate lower bound estimate of blow-up time for the solutions was obtained by discussing the properties of differential inequalities.
By constructing a new control function with small dissipative term,using energy estimate inequalities and inverse H?lder inequality,the first order nonlinear differential inequality was established about the L~p norm of the solutions of a class of nonlinear hyperbolic equations with supercritical source terms,and the accurate lower bound estimate of blow-up time for the solutions was obtained by discussing the properties of differential inequalities.
引文
[1]HUANG Wenyi,ZHANG Jian.Global Solutions and Finite Time Blow Up for Wave Equations with Both Strong and Nonlinear Damping Terms[J].Math Appl,2008,21(4):787-793.
[2]孙爱慧,曹春玲.具非线性阻尼项和源函数项双曲方程解爆破时间的下界估计[J].吉林大学学报(理学版),2014,52(6):1227-1229.(SUN Aihui,CAO Chunling.Lower Bound Estimation for the Blow-Up Time of Solutions to a Class of Nonlinear Damped Hyperbolic Equations with Sources[J].Journal of Jilin University(Science Edition),2014,52(6):1227-1229.)
[3]ZHOU Jun.Lower Bounds for Blow-Up Time of Two Nonlinear Wave Equations[J].Appl Math Lett,2015,45:64-68.
[4]吴秀兰,刘立洁,孙鹏.一类具p-Laplace算子和变指数源双曲方程解的爆破[J].吉林大学学报(理学版),2017,55(5):1177-1180.(WU Xiulan,LIU Lijie,SUN Peng.Blow-Up of Solutions to a Class of Hyperbolic Equations with p-Laplace Operator and Variable Exponential Source[J].Journal of Jilin University(Science Edition),2017,55(5):1177-1180.)
[5]GAZZOLA F,SQUASSINA M.Global Solutions and Finite Time Blow Up for Damped Semilinear Wave Equations[J].Ann Inst H PoincaréAnal Non Linéaive,2006,23(2):185-207.
[6]SUN Lili,GUO Bin,GAO Wenjie.A Lower Bound for the Blow-Up Time to a Damped Semilinear Wave Equation[J].Appl Math Lett,2014,37:22-25.
[7]GUO Bin,LIU Fang.A Lower Bound for the Blow-Up Time to a Viscoelastic Hyperbolic Equation with Nonlinear Sources[J].Appl Math Lett,2016,60:115-119.
[8]BAGHAEI K.Lower Bounds for the Blow-Up Time in a Superlinear Hyperbolic Equation with Linear Damping Term[J].Comput Math Appl,2017,73(4):560-564.
[2]孙爱慧,曹春玲.具非线性阻尼项和源函数项双曲方程解爆破时间的下界估计[J].吉林大学学报(理学版),2014,52(6):1227-1229.(SUN Aihui,CAO Chunling.Lower Bound Estimation for the Blow-Up Time of Solutions to a Class of Nonlinear Damped Hyperbolic Equations with Sources[J].Journal of Jilin University(Science Edition),2014,52(6):1227-1229.)
[3]ZHOU Jun.Lower Bounds for Blow-Up Time of Two Nonlinear Wave Equations[J].Appl Math Lett,2015,45:64-68.
[4]吴秀兰,刘立洁,孙鹏.一类具p-Laplace算子和变指数源双曲方程解的爆破[J].吉林大学学报(理学版),2017,55(5):1177-1180.(WU Xiulan,LIU Lijie,SUN Peng.Blow-Up of Solutions to a Class of Hyperbolic Equations with p-Laplace Operator and Variable Exponential Source[J].Journal of Jilin University(Science Edition),2017,55(5):1177-1180.)
[5]GAZZOLA F,SQUASSINA M.Global Solutions and Finite Time Blow Up for Damped Semilinear Wave Equations[J].Ann Inst H PoincaréAnal Non Linéaive,2006,23(2):185-207.
[6]SUN Lili,GUO Bin,GAO Wenjie.A Lower Bound for the Blow-Up Time to a Damped Semilinear Wave Equation[J].Appl Math Lett,2014,37:22-25.
[7]GUO Bin,LIU Fang.A Lower Bound for the Blow-Up Time to a Viscoelastic Hyperbolic Equation with Nonlinear Sources[J].Appl Math Lett,2016,60:115-119.
[8]BAGHAEI K.Lower Bounds for the Blow-Up Time in a Superlinear Hyperbolic Equation with Linear Damping Term[J].Comput Math Appl,2017,73(4):560-564.