Blow Up of Solutions to One Dimensional Initial-Boundary Value Problems for Semilinear Wave Equations with Variable Coefficients
被引量:5
Blow Up of Solutions to One Dimensional Initial-Boundary Value Problems for Semilinear Wave Equations with Variable Coefficients
Semilinear wave equation
critical exponent
initial-boundary value problem
blowup
lifespan.
二级参考文献14
-
1Georgiev,V.,Lindblad,H.and Sogge,C.D.,Weighted Stricharz estimates and global existence for semilinear wave equations,Amer.J.Math.,119,1997,1291-1319.
-
2Glassey,R.T.,Finite-time blow-up for solutions of nonlinear wave equations,Math.Z.,177,1981,323-340.
-
3Glassey,R.T.,Existence in the large for □u = F(u) in two space dimensions,Math.Z.,178,1981,233-261.
-
4John,F.,Blow up of solutions of nonlinear wave equations in three space dimensions,Manuscripta Math.,28,1979,235-268.
-
5Schaeffer,J.,The equation □u = |u|^p for the critical value of p,Proc.Royal Soc.Edinburgh,101,1985,31-34.
-
6Sideris,T.C.,Nonexistence of global solutions to semilinear wave equations in high dimensions,J.Differential Equations,52,1984,378-406.
-
7Strauss,W.A.,Nonlinear scattering theory at low energy,J.Funct.Anal.,41,1981,110-133.
-
8Takamura,H.,An elementary proof of the exponential blow-up for semilinear wave equations,Math.Meth.Appl.Sci,17,1994,239-249.
-
9Tataru,D.,Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equations,Trans.Amer.Math.Soc.,353,2001,795-807.
-
10Yordanov,B.T.and Zhang,Q.S.,Finite time blow up for critical wave equations in high dimensions,Journal of Funct.Anal.,231,2006,367-374.
共引文献21
-
1蔡春玲,黄守军.具有对数型衰减初值的半线性波动方程解的爆破[J].数学杂志,2020,0(1):90-98.
-
2吴密景.一类具有非紧支集初值的半线性波动方程解的爆破[J].中北大学学报(自然科学版),2013,34(5):544-547.
-
3赖宁安,陈立,马正义.Schwarzschild时空中带非线性记忆项的波动方程解的破裂[J].中国科学:数学,2015,45(2):117-128. 被引量:2
-
4韩伟,路飞.半线性波动方程柯西问题解的生命跨度的上界估计[J].数学的实践与认识,2016,46(23):263-268.
-
5Ning-An LAI,Jianli LIU,Jinglei ZHAO.Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D[J].Chinese Annals of Mathematics,Series B,2017,38(3):827-838. 被引量:4
-
6王成波.Strauss猜测相关问题与进展[J].中国科学:数学,2018,48(1):111-130. 被引量:3
-
7林银河,蒋红标,尹思露.高维半线性耗散波动方程外问题解的整体存在性[J].中国科学:数学,2018,48(4):507-518. 被引量:2
-
8韩伟,任登云.带位势项的半线性波动方程解的生命跨度的上界估计[J].火力与指挥控制,2018,43(3):116-119.
-
9汪海航,蒋红标.临界半线性波动方程解的有限时间破裂[J].浙江大学学报(理学版),2018,45(4):400-404.
-
10王虎生,孙海霞.非线性项混合的多维波动方程解的爆破研究[J].数学理论与应用,2018,38(1):48-53.
同被引文献3
-
1Yi ZHOU.Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions[J].Chinese Annals of Mathematics,Series B,2007,28(2):205-212. 被引量:22
-
2Ning-An LAI,Jianli LIU,Jinglei ZHAO.Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D[J].Chinese Annals of Mathematics,Series B,2017,38(3):827-838. 被引量:4
-
3赖宁安,周忆.Schwarzschild黑洞时空中带导数非线性项半线性波动方程解的生命跨度估计[J].中国科学:数学,2021,51(6):957-970. 被引量:2
引证文献5
-
1Ning-An LAI,Jianli LIU,Jinglei ZHAO.Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D[J].Chinese Annals of Mathematics,Series B,2017,38(3):827-838. 被引量:4
-
2范雄梅,明森,韩伟.一类带位势与散射阻尼半线性波动方程解的破裂[J].中北大学学报(自然科学版),2020,41(5):385-388.
-
3杜嘉仪,明森,韩伟,苏业芹.一类带散射阻尼项的波动方程解的破裂[J].中北大学学报(自然科学版),2021,42(6):481-485.
-
4杜嘉仪,明森,麻雅娴,杨婕.一类带阻尼项和记忆项的波动方程解的破裂[J].西华大学学报(自然科学版),2022,41(4):104-107. 被引量:1
-
5任翠,明森,麻雅娴,杨婕.外区域上Tricomi方程初边值问题解的破裂[J].华中师范大学学报(自然科学版),2024,58(2):165-171.
二级引证文献5
-
1OUYANG Bai-ping,XIAO Sheng-zhong.Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type[J].Chinese Quarterly Journal of Mathematics,2021,36(3):235-243. 被引量:1
-
2杜嘉仪,明森,麻雅娴,杨婕.一类带阻尼项和记忆项的波动方程解的破裂[J].西华大学学报(自然科学版),2022,41(4):104-107. 被引量:1
-
3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),2024,45(1):71-96.
-
4倪金凯,蒋鹏.Vlasov-Fokker-Planck-MHD方程组整体强解的存在性[J].西华大学学报(自然科学版),2024,43(3):91-96.
-
5Xiuwen LUO.Blow up for Systems of Wave Equations in Exterior Domain[J].Chinese Annals of Mathematics,Series B,2019,40(3):339-348. 被引量:1
-
1尹会成.Energy densities of semilinear wave equations with oscillatory initial data[J].Science China Mathematics,1997,40(10):1052-1064.
-
2Liu Shude~1 Chen Lihua~2 Mo Jiaqi~(1,3) (1.Dept.of Math.,Anhui Normal University,Wuhu 241000,Anhui,2.Dept.of Math.,Fuqing Branch of Fujian Normal University,Fuqing 350300,Fujian,3.Division of Computational Science,E-Institutes of Shanghai Universities,at SJTU,Shanghai 200240).THE INITIAL-BOUNDARY VALUE PROBLEMS OF NONLINEAR AND NONLOCAL SINGULARLY PERTURBED REACTION DIFFUSION SYSTEM[J].Annals of Differential Equations,2008,24(1):20-28. 被引量:5
-
3莫嘉琪.SINGULAR PERTURBATION OF INITIAL-BOUNDARY VALUE PROBLEMS FOR A CLASS OF REACTION DIFFUSION SYSTEMS[J].Applied Mathematics and Mechanics(English Edition),1991,12(4):399-408.
-
4张建文,荣晓亮,吴润衡.Initial-boundary value problems for a class of nonlinear thermoelastic plate equations[J].Chinese Physics B,2009,18(9):3693-3701.
-
5Yang,Han(杨晗),Lai,Shaoyong(赖绍永).The Local Existence for Semilinear Wave Equations[J].Journal of Southwest Jiaotong University(English Edition),2002,10(2):134-138.
-
6LIKaitai,ZHAOChunshan.Uniform attractors of non-autonomous dissipative semilinear wave equations[J].Progress in Natural Science:Materials International,2003,13(2):100-108.
-
7XuWei.BLOWUP FOR SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH SMALL INITIAL DATA[J].Journal of Partial Differential Equations,2004,17(3):198-206. 被引量:2
-
8YANG Ning YANG Han.Existence for Semilinear Wave Equations with Low Regularity[J].Chinese Quarterly Journal of Mathematics,2006,21(1):49-56.
-
9Yi ZHOU.Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions[J].Chinese Annals of Mathematics,Series B,2007,28(2):205-212. 被引量:22
-
10ZHOU YI Institute of Mathematics, Fudan University, Shanghai 200433, China..ON THE EQUATION□Φ=|▽Φ|~2 IN FOUR SPACE DIMENSIONS[J].Chinese Annals of Mathematics,Series B,2003,24(3):293-302. 被引量:2