BLOW UP OF SOLUTIONS FOR A PETROVSKY TYPE EQUATION WITH LOGARITHMIC NONLINEARITY |
Jorge, Ferreira
(Department of Exact Sciences Federal Fluminense University)
Nazli, Irkil (Department of Mathematics Dicle University) Erhan, Piskin (Department of Mathematics Dicle University) Carlos, Raposo (Department of Mathematics Federal University of Bahia) Mohammad, Shahrouzi (Department of Mathematics Jahrom University) |
1 | M. M. Al-Gharabli and S. A. Messaoudi, Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, J. Evol. Equ. 18 (2018), no. 1, 105-125. https://doi.org/10.1007/s00028-017-0392-4 DOI |
2 | I. Bialynicki-Birula and J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 23 (1975), no. 4, 461-466. |
3 | T. Cazenave and A. Haraux, Equations d'evolution avec non linearite logarithmique, Ann. Fac. Sci. Toulouse Math. (5) 2 (1980), no. 1, 21-51. DOI |
4 | W. Chen and Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal. 70 (2009), no. 9, 3203-3208. https://doi.org/10.1016/j.na.2008.04.024 DOI |
5 | H. Di, Y. Shang, and Z. 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. https://doi.org/10.1016/j.nonrwa.2019.102968 DOI |
6 | T. G. Ha and S.-H. Park, Blow-up phenomena for a viscoelastic wave equation with strong damping and logarithmic nonlinearity, Adv. Difference Equ. 2020, Paper No. 235, 17 pp. https://doi.org/10.1186/s13662-020-02694-x DOI |
7 | M. Kafini and S. Messaoudi, Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay, Appl. Anal. 99 (2020), no. 3, 530-547. https://doi.org/10.1080/00036811.2018.1504029 DOI |
8 | F. Li and Q. Gao, Blow-up of solution for a nonlinear Petrovsky type equation with memory, Appl. Math. Comput. 274 (2016), 383-392. https://doi.org/10.1016/j.amc.2015.11.018 DOI |
9 | W. Lian and R. Xu, Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term, Adv. Nonlinear Anal. 9 (2020), no. 1, 613-632. https://doi.org/10.1515/anona-2020-0016 DOI |
10 | G. Liu, The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term, Electron. Res. Arch. 28 (2020), no. 1, 263-289. https://doi.org/10.3934/era.2020016 DOI |
11 | L. Liu, F. Sun, and Y. Wu, Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level, Bound. Value Probl. 2019 (2019), Paper No. 15, 18 pp. https://doi.org/10.1186/s13661-019-1136-x DOI |
12 | L. Liu, F. Sun, and Y. Wu, Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy, Partial Differ. Equ. Appl. 1 (2020), no. 5, Paper No. 31, 18 pp. https://doi.org/10.1007/s42985-020-00031-1 DOI |
13 | S. A. Messaoudi, Global existence and nonexistence in a system of Petrovsky, J. Math. Anal. Appl. 265 (2002), no. 2, 296-308. https://doi.org/10.1006/jmaa.2001.7697 DOI |
14 | S.-H. Park, Blowup for nonlinearly damped viscoelastic equations with logarithmic source and delay terms, Adv. Difference Equ. 2021 (2021), Paper No. 316, 14 pp. https://doi.org/10.1186/s13662-021-03469-8 DOI |
15 | I. G. Petrovsky, Uber das Cauchysche Problem fur Systeme von partiellen Differential-gleichungen, Mat. sb. (Mosk.) 44 (1937), no. 5, 815-870. |
16 | I. G. Petrowsky, Sur l'analyticite des solutions des systemes d'equations differentielles, Rec. Math. N. S. [Mat. Sbornik] 5(47) (1939), 3-70. |
17 | E. Piskin and N. Irkil, Blow up of the solution for hyperbolic type equation with logarithmic nonlinearity, Aligarh Bull. Math. 39 (2020), no. 1, 43-53. |
18 | E. Piskin and N. Irkil, Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 70 (2021), no. 1, 300-319. DOI |
19 | F. Tahamtani and M. Shahrouzi, Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term, Bound. Value Probl. 2012 (2012), 50, 15 pp. https://doi.org/10.1186/1687-2770-2012-50 DOI |
20 | E. Piskin and N. Polat, On the decay of solutions for a nonlinear Petrovsky equation, Math. Sci. Letters. 3 (2014), no. 1, 43-47. DOI |
21 | Y. Ye, Global solution and blow-up of logarithmic Klein-Gordon equation, Bull. Korean Math. Soc. 57 (2020), no. 2, 281-294. https://doi.org/10.4134/BKMS.b190190 DOI |
22 | M. M. Al-Gharabli, A. Guesmia, and S. A. Messaoudi, Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity, Commun. Pure Appl. Anal. 18 (2019), no. 1, 159-180. https://doi.org/10.3934/cpaa.2019009 DOI |
23 | F. Alabau-Boussouira, P. Cannarsa, and D. Sforza, Decay estimates for second order evolution equations with memory, J. Funct. Anal. 254 (2008), no. 5, 1342-1372. https://doi.org/10.1016/j.jfa.2007.09.012 DOI |
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