-
Previous Article
On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay
- EECT Home
- This Issue
-
Next Article
Decay rate of global solutions to three dimensional generalized MHD system
Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy
School of Mathematics, Jilin University, Changchun 130012, China |
$ u_{tt}-\Delta u-\Delta u_{t} = |u|^{p-2}u\log|u|, $ |
$ L^{2}(\Omega) $ |
References:
[1] |
J. M. Ball,
Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford Ser., 28 (1977), 473-486.
doi: 10.1093/qmath/28.4.473. |
[2] |
H. Chen and S. Y. Tian,
Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity, J. Differential Equations, 258 (2015), 4424-4442.
doi: 10.1016/j.jde.2015.01.038. |
[3] |
Y. Cao and C. H. Liu, Initial boundary value problem for a mixed pseudo-parabolic $p$-Laplacian type equation with logarithmic nonlinearity, Electron. J. Differential Equations, (2018), Paper No. 116, 1–19. |
[4] |
P. Dai, C. L. Mu and G. Y. Xu, Blow-up phenomena for a pseudo-parabolic equation with $p$-Laplacian and Logarithmic nonlinearity terms, J. Math. Anal. Appl., 481 (2020), no. 1, 123439, 27 pp.
doi: 10.1016/j.jmaa.2019.123439. |
[5] |
H. F. Di, Y. D. Shang and Z. F. Song, Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity, Nonlinear Anal. Real World Appl., 51 (2020), 102968, 22 pp.
doi: 10.1016/j.nonrwa.2019.102968. |
[6] |
P. Górka,
Logarithmic Klein-Gordon equation, Acta Phys. Polon. B, 40 (2009), 59-66.
|
[7] |
B. Guo and F. Liu,
A lower bound for the blow-up time to a viscoelastic hyperbolic equation with nonlinear sources, Appl. Math. Lett., 60 (2016), 115-119.
doi: 10.1016/j.aml.2016.03.017. |
[8] |
Y. J. He, H. H. Gao and H. Wang,
Blow-up and decay for a class of pseudo-parabolic $p$-Laplacian equation with logarithmic nonlinearity, Comput. Math. Appl., 75 (2018), 459-469.
doi: 10.1016/j.camwa.2017.09.027. |
[9] |
M. A. Hamza and H. Zaag, The blow-up rate for a non-scaling invariant semilinear wave equations, J. Math. Anal. Appl., 483 (2020), 123652, 34 pp.
doi: 10.1016/j.jmaa.2019.123652. |
[10] |
C. N. Le and X. T. Le,
Global solution and blow-up for a class of $p$-Laplacian evolution equations with logarithmic nonlinearity, Acta Appl. Math., 151 (2017), 149-169.
doi: 10.1007/s10440-017-0106-5. |
[11] |
H. A. Levine, Remarks on the growth and nonexistence of solutions to nonlinear wave equations, A Seminar on PDEs - 1973, Rutgers Univ., New Brunswick, N. J., 1973, 59–70. |
[12] |
H. A. Levine,
Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal., 5 (1974), 138-146.
doi: 10.1137/0505015. |
[13] |
H. A. Levine,
Instability and nonexistence of global solutions to nonlinear wave equations of the form $Pu_tt=-Au+F(u)$, Trans. Amer. Math. Soc., 192 (1974), 1-21.
doi: 10.2307/1996814. |
[14] |
L. W. Ma and Z. B. Fang,
Energy decay estimates and infinite blow-up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source, Math. Methods Appl. Sci., 41 (2018), 2639-2653.
doi: 10.1002/mma.4766. |
[15] |
L. C. Nhan and L. X. Truong,
Global solution and blow-up for a class of pseudo $p$-Laplacian evolution equations with logarithmic nonlinearity, Comput. Math. Appl., 73 (2017), 2076-2091.
doi: 10.1016/j.camwa.2017.02.030. |
[16] |
V. Pata and S. Zelik,
Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 1495-1506.
doi: 10.1088/0951-7715/19/7/001. |
[17] |
L. L. Sun, B. Guo and W. J. Gao,
A lower bound for the blow-up time to a damped semilinear wave equation, Appl. Math. Lett., 37 (2014), 22-25.
doi: 10.1016/j.aml.2014.05.009. |
[18] |
J. Zhou,
Lower bounds for blow-up time of two nonlinear wave equations, Appl. Math. Lett., 45 (2015), 64-68.
doi: 10.1016/j.aml.2015.01.010. |
show all references
References:
[1] |
J. M. Ball,
Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford Ser., 28 (1977), 473-486.
doi: 10.1093/qmath/28.4.473. |
[2] |
H. Chen and S. Y. Tian,
Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity, J. Differential Equations, 258 (2015), 4424-4442.
doi: 10.1016/j.jde.2015.01.038. |
[3] |
Y. Cao and C. H. Liu, Initial boundary value problem for a mixed pseudo-parabolic $p$-Laplacian type equation with logarithmic nonlinearity, Electron. J. Differential Equations, (2018), Paper No. 116, 1–19. |
[4] |
P. Dai, C. L. Mu and G. Y. Xu, Blow-up phenomena for a pseudo-parabolic equation with $p$-Laplacian and Logarithmic nonlinearity terms, J. Math. Anal. Appl., 481 (2020), no. 1, 123439, 27 pp.
doi: 10.1016/j.jmaa.2019.123439. |
[5] |
H. F. Di, Y. D. Shang and Z. F. Song, Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity, Nonlinear Anal. Real World Appl., 51 (2020), 102968, 22 pp.
doi: 10.1016/j.nonrwa.2019.102968. |
[6] |
P. Górka,
Logarithmic Klein-Gordon equation, Acta Phys. Polon. B, 40 (2009), 59-66.
|
[7] |
B. Guo and F. Liu,
A lower bound for the blow-up time to a viscoelastic hyperbolic equation with nonlinear sources, Appl. Math. Lett., 60 (2016), 115-119.
doi: 10.1016/j.aml.2016.03.017. |
[8] |
Y. J. He, H. H. Gao and H. Wang,
Blow-up and decay for a class of pseudo-parabolic $p$-Laplacian equation with logarithmic nonlinearity, Comput. Math. Appl., 75 (2018), 459-469.
doi: 10.1016/j.camwa.2017.09.027. |
[9] |
M. A. Hamza and H. Zaag, The blow-up rate for a non-scaling invariant semilinear wave equations, J. Math. Anal. Appl., 483 (2020), 123652, 34 pp.
doi: 10.1016/j.jmaa.2019.123652. |
[10] |
C. N. Le and X. T. Le,
Global solution and blow-up for a class of $p$-Laplacian evolution equations with logarithmic nonlinearity, Acta Appl. Math., 151 (2017), 149-169.
doi: 10.1007/s10440-017-0106-5. |
[11] |
H. A. Levine, Remarks on the growth and nonexistence of solutions to nonlinear wave equations, A Seminar on PDEs - 1973, Rutgers Univ., New Brunswick, N. J., 1973, 59–70. |
[12] |
H. A. Levine,
Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal., 5 (1974), 138-146.
doi: 10.1137/0505015. |
[13] |
H. A. Levine,
Instability and nonexistence of global solutions to nonlinear wave equations of the form $Pu_tt=-Au+F(u)$, Trans. Amer. Math. Soc., 192 (1974), 1-21.
doi: 10.2307/1996814. |
[14] |
L. W. Ma and Z. B. Fang,
Energy decay estimates and infinite blow-up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source, Math. Methods Appl. Sci., 41 (2018), 2639-2653.
doi: 10.1002/mma.4766. |
[15] |
L. C. Nhan and L. X. Truong,
Global solution and blow-up for a class of pseudo $p$-Laplacian evolution equations with logarithmic nonlinearity, Comput. Math. Appl., 73 (2017), 2076-2091.
doi: 10.1016/j.camwa.2017.02.030. |
[16] |
V. Pata and S. Zelik,
Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 1495-1506.
doi: 10.1088/0951-7715/19/7/001. |
[17] |
L. L. Sun, B. Guo and W. J. Gao,
A lower bound for the blow-up time to a damped semilinear wave equation, Appl. Math. Lett., 37 (2014), 22-25.
doi: 10.1016/j.aml.2014.05.009. |
[18] |
J. Zhou,
Lower bounds for blow-up time of two nonlinear wave equations, Appl. Math. Lett., 45 (2015), 64-68.
doi: 10.1016/j.aml.2015.01.010. |
[1] |
Menglan Liao. The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity. Evolution Equations and Control Theory, 2022, 11 (3) : 781-792. doi: 10.3934/eect.2021025 |
[2] |
Yuzhu Han, Qi Li. Lifespan of solutions to a damped plate equation with logarithmic nonlinearity. Evolution Equations and Control Theory, 2022, 11 (1) : 25-40. doi: 10.3934/eect.2020101 |
[3] |
Tarek Saanouni. Global well-posedness of some high-order semilinear wave and Schrödinger type equations with exponential nonlinearity. Communications on Pure and Applied Analysis, 2014, 13 (1) : 273-291. doi: 10.3934/cpaa.2014.13.273 |
[4] |
Irena Lasiecka, Roberto Triggiani. Global exact controllability of semilinear wave equations by a double compactness/uniqueness argument. Conference Publications, 2005, 2005 (Special) : 556-565. doi: 10.3934/proc.2005.2005.556 |
[5] |
Bilgesu A. Bilgin, Varga K. Kalantarov. Non-existence of global solutions to nonlinear wave equations with positive initial energy. Communications on Pure and Applied Analysis, 2018, 17 (3) : 987-999. doi: 10.3934/cpaa.2018048 |
[6] |
Salim A. Messaoudi, Ala A. Talahmeh. Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1233-1245. doi: 10.3934/dcdss.2021107 |
[7] |
Dongbing Zha, Yi Zhou. The lifespan for quasilinear wave equations with multiple propagation speeds in four space dimensions. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1167-1186. doi: 10.3934/cpaa.2014.13.1167 |
[8] |
Kyouhei Wakasa. The lifespan of solutions to semilinear damped wave equations in one space dimension. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1265-1283. doi: 10.3934/cpaa.2016.15.1265 |
[9] |
Jie Yang, Sen Ming, Wei Han, Xiongmei Fan. Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022022 |
[10] |
Hui Yang, Yuzhu Han. Initial boundary value problem for a strongly damped wave equation with a general nonlinearity. Evolution Equations and Control Theory, 2022, 11 (3) : 635-648. doi: 10.3934/eect.2021019 |
[11] |
Yannick Privat, Emmanuel Trélat, Enrique Zuazua. Complexity and regularity of maximal energy domains for the wave equation with fixed initial data. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 6133-6153. doi: 10.3934/dcds.2015.35.6133 |
[12] |
Gisèle Ruiz Goldstein, Jerome A. Goldstein, Fabiana Travessini De Cezaro. Equipartition of energy for nonautonomous wave equations. Discrete and Continuous Dynamical Systems - S, 2017, 10 (1) : 75-85. doi: 10.3934/dcdss.2017004 |
[13] |
Yuxuan Chen, Jiangbo Han. Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4179-4200. doi: 10.3934/dcdss.2021109 |
[14] |
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Jian Zhang. Sequences of high and low energy solutions for weighted (p, q)-equations. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022114 |
[15] |
Hua Chen, Huiyang Xu. Global existence and blow-up of solutions for infinitely degenerate semilinear pseudo-parabolic equations with logarithmic nonlinearity. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1185-1203. doi: 10.3934/dcds.2019051 |
[16] |
Wenjun Liu, Jiangyong Yu, Gang Li. Global existence, exponential decay and blow-up of solutions for a class of fractional pseudo-parabolic equations with logarithmic nonlinearity. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4337-4366. doi: 10.3934/dcdss.2021121 |
[17] |
Marcello D'Abbicco, Giovanni Girardi, Giséle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Equipartition of energy for nonautonomous damped wave equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (2) : 597-613. doi: 10.3934/dcdss.2020364 |
[18] |
Carlos E. Kenig. The method of energy channels for nonlinear wave equations. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 6979-6993. doi: 10.3934/dcds.2019240 |
[19] |
Bi Ping, Maoan Han. Oscillation of second order difference equations with advanced argument. Conference Publications, 2003, 2003 (Special) : 108-112. doi: 10.3934/proc.2003.2003.108 |
[20] |
Xiaoqiang Dai, Chao Yang, Shaobin Huang, Tao Yu, Yuanran Zhu. Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems. Electronic Research Archive, 2020, 28 (1) : 91-102. doi: 10.3934/era.2020006 |
2021 Impact Factor: 1.169
Tools
Metrics
Other articles
by authors
[Back to Top]