
تعداد نشریات | 21 |
تعداد شمارهها | 651 |
تعداد مقالات | 9,504 |
تعداد مشاهده مقاله | 68,341,927 |
تعداد دریافت فایل اصل مقاله | 47,847,139 |
Global existence and blow-up results for a nonlinear viscoelastic higher-order p(x)-Laplacian equation | ||
International Journal of Nonlinear Analysis and Applications | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 12 شهریور 1404 اصل مقاله (430.96 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.35644.5299 | ||
نویسنده | ||
Mohammad Shahrouzi* | ||
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
تاریخ دریافت: 25 مهر 1403، تاریخ بازنگری: 26 آبان 1403، تاریخ پذیرش: 30 دی 1403 | ||
چکیده | ||
This study aims for the global existence and blow-up of solutions for a class of nonlinear viscoelastic higher-order $p(x)$-Laplacian equations. First, we prove the global existence of solutions in the appropriate range of the variable exponents and next, by using different methods, we prove the blow-up of solutions with positive and negative initial energy. Our results are new, and it is the first time that taken into consideration, extending and improving the earlier results in the literature, such as (Bol. Soc. Mat. Mex.., 2023, https://doi.org/10.1007/s40590-023-00551-x). | ||
کلیدواژهها | ||
global existence؛ blow-up؛ higher-order؛ viscoelastic؛ $p(x)$-Laplacian | ||
مراجع | ||
[1] S. Antontsev and S. Shmarev, Evolution PDEs with Nonstandard Growth Conditions: Existence, Uniqueness, Localization, Blow-Up, in: Atlantis Studies in Differential Equations. Atlantis Press, Paris, 2015. [2] B. Belhadji, J. Alzabut, M. E. Samei, and N. Fatima, On the global behaviour of solutions for a delayed viscoelastic[1]type Petrovesky wave equation with p-Laplacian operator and logarithmic source, Mathematics 10 (2022), no. 4194, 1–39. [3] A. Benaissa and S. Mokeddem, Decay estimates for the wave equation of p-Laplacian type with dissipation of m-Laplacian type, Math. Meth. Appl. Sci. 30 (2007), 237–247. [4] T. Boudjeriou, On the diffusion p(x)-Laplacian with logarithmic nonlinearity, J. Elliptic Parabol. Equ. 6 (2020), 773–794. [5] W. Boughamsaa and A. Ouaoua, Local well-posedness and blow-up of solution for a higher-order wave equation with viscoelastic term and variable-exponent, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 4, 111–124. [6] N. Boumaza, B. Gheraibia, and G. Liu, Global well-posedness of solutions for the p-Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity, Taiwan. J. Math. 26 (2022), no. 6, 1235–1255. [7] W. Bu, T. An, Y. Li, and J. He, Kirchhoff-type problems involving logarithmic nonlinearity with variable exponent and convection term, Mediterr. J. Math. 20 (2023), no. 77, 1–22. [8] Y. Chu, Y. Wu, and L. Cheng, Blow up and decay for a class of p-Laplacian hyperbolic equation with logarithmic nonlinearity, Taiwan. J. Math. 26 (2022), no. 4, 741–763. [9] L. Diening, P. Hasto, P. Harjulehto, and M. M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, 2011. [10] J. Ferreira, N. Irkıil, E. Pi¸skin, C. A. Raposo, and M. Shahrouzi, Blow up of solutions for a Petrovsky type equation with logarithmic nonlinearity, Bull. Korean Math. Soc. 46 (2022), 1495–1510. [11] J. Ferreira, W. S. Panni, S. A. Messaoudi, E. Piskin, and M. Shahrouzi, Existence and asymptotic behavior of beam-equation solutions with strong damping and p(x)-biharmonic operator, J. Math. Phys. Anal. Geom. 18 (2022), no. 4, 488–513. [12] J. Ferreira, W. S. Panni, E. Piskin, and M. Shahrouzi, Existence of beam-equation solutions with strong damping and p(x)-biharmonic operator, Math. Moravica 26 (2022), no. 2, 123–145. [13] M. Kafini and M. Noor, Delayed wave equation with logarithmic variable-exponent nonlinearity, ERA 31 (2023), no. 5, 2974–2993. [14] J. R. Kang, General decay for viscoelastic plate equation with p-Laplacian and time-varying delay, Bound. Value Probl. 2018 (2018), no. 29, 1–11. [15] N. J. Kass and M. H. Rammaha, On wave equations of the p-Laplacian type with supercritical nonlinearities, Nonlinear Anal. 183 (2019), 70–101. [16] R. Pan, Y. Gao, and Q. Meng, Properties of weak solutions for a pseudoparabolic equation with logarithmic nonlinearity of variable exponents, J. Math. 2023 (2023), no. 7441168, 1–9. [17] P. Pei, M. A. Rammaha, and D. Toundykov, Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources, J. Math. Phys. 56 (2015), no. 081503, 1–30. [18] D. C. Pereira, G. M. Araujo, C. A. Raposo, and V. R. Cabanillas, Blow-up results for a viscoelastic beam equation of p-Laplacian type with strong damping and logarithmic source, Math. Meth. Appl. Sci. 46 (2023), 8831–8854. [19] E. Pi¸skin, S. Boulaaras, and N. Irkıil, Qualitative analysis of solutions for the p-Laplacian hyperbolic equation with logarithmic nonlinearity, Math. Meth. Appl. Sci. 44 (2021), no. 6, 4654–4672. [20] E. Piskin and N. Irkıil, Mathematical behavior of solutions of p-Laplacian equation with logarithmic source term, Sigma J. Eng. Nat. Sci. 10 (2019), no. 2, 213–220. [21] E. Piskin and N. Irkıil, Local existence and blow up for p-Laplacian equation with logarithmic nonlinearity, Conf. Proc. Sci. Technol. 3 (2020), no. 1, 150–155. [22] E. Piskin and N. Irkıil, 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. [23] E. Pi¸skin and H. Yuksekkaya, Nonexistence of solutions for a higher-order wave equation with delay and variable[1]exponents, In: Ray, S.S., Jafari, H., Sekhar, T.R., Kayal, S. (eds) Applied Analysis, Computation and Mathe[1]matical Modelling in Engineering. AACMME 2021. Lecture Notes in Electrical Engineering, vol 897. Springer, Singapore (2022). [24] C. A. Raposo, A. P. Cattai, and J. O. Ribeiro, Global solution and asymptotic behaviour for a wave equation type p-Laplacian with memory, Open J. Math. Anal. 2 (2018), no. 2, 156–171. [25] M. Shahrouzi, Blow-up analysis for a class of higher-order viscoelastic inverse problem with positive initial energy and boundary feedback, Ann. Mat. 196 (2017), 1877–1886. [26] M. Shahrouzi, On behaviour of solutions for a nonlinear viscoelastic equation with variable-exponent nonlinearities, Comput. Math. with Appl. 75 (2018), no. 11, 3946–3956. [27] M. Shahrouzi, Blow up of solutions for a r(x)-Laplacian Lame equation with variable-exponent nonlinearities and arbitrary initial energy level, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 441–450. [28] M. Shahrouzi, General decay and blow up of solutions for a class of inverse problem with elasticity term and variable[1]exponent nonlinearities, Math. Meth. Appl. Sci. 45 (2022), no. 4, 1864–1878. [29] M. Shahrouzi, Asymptotic behavior of solutions for a nonlinear viscoelastic higher-order p(x)-Laplacian equation with variable-exponent logarithmic source term, Bol. Soc. Mat. Mex. 29 (2023), no. 77, 1–20. [30] M. Shahrouzi, J. Ferreira, and E. Piskin, Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term, Ric. Mat. (2022), 1–25. [31] M. Shahrouzi and F. Kargarfard, Blow-up of solutions for a Kirchhoff type equation with variable-exponent nonlinearities, J. Appl. Anal. 27 (2021), no. 1, 97–105. [32] Y. Wu and X. Xue, Decay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving p-Laplacian, J. Math. Phys. 55 (2014), no. 121504, 1–23. [33] H. Yang and Y. Han, Blow-up for a damped p-Laplacian type wave equation with logarithmic nonlinearity, J. Differ. Equ. 306 (2022), 569–589. [34] Y. Ye, Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term, Nonlinear Anal. 112 (2015), 129–146. [35] F. Zeng, Q. Deng, and D. Wang, Global existence and blow-up for the pseudo-parabolic p(x)-Laplacian equation with logarithmic nonlinearity, J. Nonlinear Math. Phys. 29 (2022), 41–57. [36] Z. Zennir, A. Beniani, B. Bochra, and L. Alkhalifa, Destruction of solutions for class of wave p(x)-bi-Laplace equation with nonlinear dissipation, AIMS Math. 8 (2022), no. 1, 285–294. [37] G. Zu, L. Sun, and J. Wu, Global existence and blow-up for wave equation of p-Laplacian type, Anal. Math. Phys. 13 (2023), no. 53, 1–22. | ||
آمار تعداد مشاهده مقاله: 15 تعداد دریافت فایل اصل مقاله: 7 |