Blow up and growth of solutions to a viscoelastic parabolic type Kirchhoff equation with Variable-exponents in the Damping and Source terms
Blow up and growth of solutions to a viscoelastic parabolic
Resumo
In this paper, we consider a Kirchhoff-type viscoelastic equation with nonlinear damping and source terms involving variable exponents. We
establish results on the blow-up and exponential growth of solutions corresponding to negative initial energy.
Downloads
Não há dados estatísticos.
Referências
[1] Antontsev, Stanislav, Jorge Ferreira, and Erhan Piskin. "Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities."(2021):
[2] Baghaei, Khadijeh, Mohammad Bagher Ghaemi, and Mahmoud Hesaaraki. "Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source." Applied Mathematics Letters 27(2014) : 49 52:
[3] BAlves, Claudianor O., Marcelo M. Cavalcanti, Valeria N. Domingos Cavalcanti, Mohammad A. Rammaha, and Daniel Toundykov. "On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms." Discrete and Continuous Dynamical Systems¿ Series S 2, no.3(2009) : 583:
[4] Dang, Jian, Qingying Hu, Suxia Xia, and Hongwei Zhang. "Exponential growth of solution for a class of reaction di¤usion equation with memory and multiple nonlinearities." Research in Applied Mathematics 1 (2017): 1-9.
[5] Diening, Lars, Petteri Harjulehto, PBAeter Hästö, and Michael R°uµziµcka. Lebesgue and Sobolev spaces with variable exponents. Springer, 2011.
[6] Dohemeto, Fortuné Mahougnon, Guy Aymard Degla, and Cyrille Sègbégnon Dansou. "BLOW-UP AND GLOBAL EXISTENCE OF SOLUTIONS FOR HIGHER-ORDER KIRCHHOFF-TYPE EQUATIONS WITH VARIABLE EXPONENTS." Journal of Mahani Mathematical Research 11, no.3(2022) : 109 131.
[7] Ekinci, Fatma, and Erhan PI¸SK · IN. · "Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term." Mathematical Sciences and Applications E-Notes 11, no:3(2023) : 153 163.
[8] Khaldi, Aya, Amar Ouaoua, and Messaoud Maouni. "Global existence and stability of solution for a nonlinear Kirchho¤ type reaction-di¤usion equation with variable exponents."
Mathematica Bohemica 147, no. 4(2022) : 471 484.
[9] Diening, Lars, et al. Lebesgue and Sobolev spaces with variable exponents. Springer, 2011.
[10] Messaoudi, Salim A., Mohammad M. Al-Gharabli, Adel M. Al-Mahdi, and Mohammed A. Al-Osta. "A coupled system of Laplacian and bi-Laplacian equations with nonlinear dampings and source terms of variable-exponents nonlinearities: Existence, uniqueness, blowup and a large-time asymptotic behavior." AIMS Mathematics 8, no.4(2023) : 7933 7966:
[11] Messaoudi, Salim A., and Ala A. Talahmeh. "Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities." Discrete & Continuous Dynamical Systems-Series S 15, no.5 (2022).
[12] Park, Sun-Hye, and Jum-Ran Kang. "Blow-up of solutions for a viscoelastic wave equation with variable exponents." Mathematical Methods in the Applied Sciences 42, no:6(2019) : 2083 2097.
[13] Piskin, Erhan, and Fatma Ekinci. "Qualitative analysis of solutions for a Kirchhoff-type parabolic equation with multiple nonlinearities." Hacettepe Journal of Mathematics and Statistics 50, no. 2(2021) : 397 413.
[14] Piskin Erhan, and Fatma Ekinci."Blow up, exponential growth of solution for a reactiondi¤usion equation with multiple nonlinearities." Tbilisi Mathematical Journal 12, no. 4(2019) : 61 70.
[15] Piskin Erhan, and Fatma Ekinci. "Blow up and growth of solutions for a parabolic type Kirchho¤ equation with multiple nonlinearities." Konuralp Journal of Mathematics 8, no.1(2020) : 216 222.
[16] Piskin, Erhan. "Finite time blow up of solutions of the Kirchho¤-type equation with variable exponents." International Journal of Nonlinear Analysis and Applications 11, no.1(2020) : 37 45.
[17] Piskin, Erhan, and Gülistan BUTAKIN. "Existence and Decay of Solutions for a Parabolic-Type Kirchho¤ Equation with Variable Exponents." Journal of Mathematical Sciences and Modelling 6, no. 1 (2023) : 32 41.
[18] Piskin, Erhan, and Nebi Y¬lmaz. "Blow up of solutions for a system of strongly damped Petrovsky equations with variable exponents." Acta Universitatis Apulensis 71(2022) : 8799.
[19] Piskin, Erhan, and Fatma Ekinci. "Nonexistence and growth of solutions for a parabolic p-Laplacian system." Sigma 10, no. 3 (2019): 301-307.
[20] Piskin, Erhan, and Fatma Ekinci. "Blow up and growth of solutions to a viscoelastic parabolic type Kirchho¤ equation." Filomat 37, no.2(2023): 519-530.
[21] Piskin, Erhan, and Nebi Yilmaz. "Nonexistence of global solutions for a system of Kirchhoff-type equations with variable exponents." The Aligarh Bulletin of Mathematics Volume 41, Number 2 (2022); 103 116.
[22] Yavuz, D. I. N.Ç, and Erhan P¸SKIN. · "Upper bounds for the blow up time for the Kirchhoff-type equation." Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no.2(2022) : 352 362. [23] Qu, Chengyuan, Wenshu Zhou, and Bo Liang. [11] "Asymptotic behavior for a fourthorder parabolic equation modeling thin …lm growth." Applied Mathematics Letters 78(2018) : 141 146:
[24] Shahrouzi, Mohammad. "Exponential growth of solutions for a variable-exponent fourthorder viscoelastic equation with nonlinear boundary feedback." Facta Universitatis, Series: Mathematics and Informatics (2022) : 507 520.
[25] Shahrouzi, Mohammad, et al. "Blow-up analysis for a class of plate viscoelastic p(x)- Kirchho¤ type inverse source problem with variable-exponent nonlinearities." Siberian Electron. Math. Report., 19(2)(2022); 912 934:
[26] Tebba, Zakia, Hakima Degaichia, Mohamed Abdalla, Bahri Belkacem Cherif, and Ibrahim Mekawy. "Blow-Up of Solutions for a Class Quasilinear Wave Equation with Nonlinearity Variable Exponents." Journal of Function Spaces 2021(2021) : 1 9.
[27] Truong, Le Xuan, and Nguyen Van Y. "Exponential growth with Lp-norm of solutions for nonlinear heat equations with viscoelastic term." Applied Mathematics and Computation 273 (2016) : 656 663.
[28] Wang, Hua, and Yijun He. "On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy." Applied Mathematics Letters 26:10(2013) : 1008 1012:
[29] Wu, Xiulan, Bin Guo, and Wenjie Gao. "Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy." Applied Mathematics Letters 26:5(2013) : 539 543.
[30] Wu, Yuyu, and Yunzhu Gao. "Blow up of solutions of Kirchho¤ type viscoelastic wave equations with logarithmic nonlinearity of variable exponents." (2023)
[2] Baghaei, Khadijeh, Mohammad Bagher Ghaemi, and Mahmoud Hesaaraki. "Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source." Applied Mathematics Letters 27(2014) : 49 52:
[3] BAlves, Claudianor O., Marcelo M. Cavalcanti, Valeria N. Domingos Cavalcanti, Mohammad A. Rammaha, and Daniel Toundykov. "On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms." Discrete and Continuous Dynamical Systems¿ Series S 2, no.3(2009) : 583:
[4] Dang, Jian, Qingying Hu, Suxia Xia, and Hongwei Zhang. "Exponential growth of solution for a class of reaction di¤usion equation with memory and multiple nonlinearities." Research in Applied Mathematics 1 (2017): 1-9.
[5] Diening, Lars, Petteri Harjulehto, PBAeter Hästö, and Michael R°uµziµcka. Lebesgue and Sobolev spaces with variable exponents. Springer, 2011.
[6] Dohemeto, Fortuné Mahougnon, Guy Aymard Degla, and Cyrille Sègbégnon Dansou. "BLOW-UP AND GLOBAL EXISTENCE OF SOLUTIONS FOR HIGHER-ORDER KIRCHHOFF-TYPE EQUATIONS WITH VARIABLE EXPONENTS." Journal of Mahani Mathematical Research 11, no.3(2022) : 109 131.
[7] Ekinci, Fatma, and Erhan PI¸SK · IN. · "Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term." Mathematical Sciences and Applications E-Notes 11, no:3(2023) : 153 163.
[8] Khaldi, Aya, Amar Ouaoua, and Messaoud Maouni. "Global existence and stability of solution for a nonlinear Kirchho¤ type reaction-di¤usion equation with variable exponents."
Mathematica Bohemica 147, no. 4(2022) : 471 484.
[9] Diening, Lars, et al. Lebesgue and Sobolev spaces with variable exponents. Springer, 2011.
[10] Messaoudi, Salim A., Mohammad M. Al-Gharabli, Adel M. Al-Mahdi, and Mohammed A. Al-Osta. "A coupled system of Laplacian and bi-Laplacian equations with nonlinear dampings and source terms of variable-exponents nonlinearities: Existence, uniqueness, blowup and a large-time asymptotic behavior." AIMS Mathematics 8, no.4(2023) : 7933 7966:
[11] Messaoudi, Salim A., and Ala A. Talahmeh. "Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities." Discrete & Continuous Dynamical Systems-Series S 15, no.5 (2022).
[12] Park, Sun-Hye, and Jum-Ran Kang. "Blow-up of solutions for a viscoelastic wave equation with variable exponents." Mathematical Methods in the Applied Sciences 42, no:6(2019) : 2083 2097.
[13] Piskin, Erhan, and Fatma Ekinci. "Qualitative analysis of solutions for a Kirchhoff-type parabolic equation with multiple nonlinearities." Hacettepe Journal of Mathematics and Statistics 50, no. 2(2021) : 397 413.
[14] Piskin Erhan, and Fatma Ekinci."Blow up, exponential growth of solution for a reactiondi¤usion equation with multiple nonlinearities." Tbilisi Mathematical Journal 12, no. 4(2019) : 61 70.
[15] Piskin Erhan, and Fatma Ekinci. "Blow up and growth of solutions for a parabolic type Kirchho¤ equation with multiple nonlinearities." Konuralp Journal of Mathematics 8, no.1(2020) : 216 222.
[16] Piskin, Erhan. "Finite time blow up of solutions of the Kirchho¤-type equation with variable exponents." International Journal of Nonlinear Analysis and Applications 11, no.1(2020) : 37 45.
[17] Piskin, Erhan, and Gülistan BUTAKIN. "Existence and Decay of Solutions for a Parabolic-Type Kirchho¤ Equation with Variable Exponents." Journal of Mathematical Sciences and Modelling 6, no. 1 (2023) : 32 41.
[18] Piskin, Erhan, and Nebi Y¬lmaz. "Blow up of solutions for a system of strongly damped Petrovsky equations with variable exponents." Acta Universitatis Apulensis 71(2022) : 8799.
[19] Piskin, Erhan, and Fatma Ekinci. "Nonexistence and growth of solutions for a parabolic p-Laplacian system." Sigma 10, no. 3 (2019): 301-307.
[20] Piskin, Erhan, and Fatma Ekinci. "Blow up and growth of solutions to a viscoelastic parabolic type Kirchho¤ equation." Filomat 37, no.2(2023): 519-530.
[21] Piskin, Erhan, and Nebi Yilmaz. "Nonexistence of global solutions for a system of Kirchhoff-type equations with variable exponents." The Aligarh Bulletin of Mathematics Volume 41, Number 2 (2022); 103 116.
[22] Yavuz, D. I. N.Ç, and Erhan P¸SKIN. · "Upper bounds for the blow up time for the Kirchhoff-type equation." Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no.2(2022) : 352 362. [23] Qu, Chengyuan, Wenshu Zhou, and Bo Liang. [11] "Asymptotic behavior for a fourthorder parabolic equation modeling thin …lm growth." Applied Mathematics Letters 78(2018) : 141 146:
[24] Shahrouzi, Mohammad. "Exponential growth of solutions for a variable-exponent fourthorder viscoelastic equation with nonlinear boundary feedback." Facta Universitatis, Series: Mathematics and Informatics (2022) : 507 520.
[25] Shahrouzi, Mohammad, et al. "Blow-up analysis for a class of plate viscoelastic p(x)- Kirchho¤ type inverse source problem with variable-exponent nonlinearities." Siberian Electron. Math. Report., 19(2)(2022); 912 934:
[26] Tebba, Zakia, Hakima Degaichia, Mohamed Abdalla, Bahri Belkacem Cherif, and Ibrahim Mekawy. "Blow-Up of Solutions for a Class Quasilinear Wave Equation with Nonlinearity Variable Exponents." Journal of Function Spaces 2021(2021) : 1 9.
[27] Truong, Le Xuan, and Nguyen Van Y. "Exponential growth with Lp-norm of solutions for nonlinear heat equations with viscoelastic term." Applied Mathematics and Computation 273 (2016) : 656 663.
[28] Wang, Hua, and Yijun He. "On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy." Applied Mathematics Letters 26:10(2013) : 1008 1012:
[29] Wu, Xiulan, Bin Guo, and Wenjie Gao. "Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy." Applied Mathematics Letters 26:5(2013) : 539 543.
[30] Wu, Yuyu, and Yunzhu Gao. "Blow up of solutions of Kirchho¤ type viscoelastic wave equations with logarithmic nonlinearity of variable exponents." (2023)
Publicado
2026-01-21
Seção
Artigos
Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
