[1] Barbu, V., Lasiecka, I., Rammaha, M. A.: Existence and uniqueness of solutions to wave equations with nonlinear
degenerate damping and source terms. Control Cybernetics. 34(3), 665-687 (2005).
[2] Nishihara, K., Yamada, Y.: On global solutions of some degenerate quasilinear hyperbolic equations with dissipative
terms. Funkcialaj Ekvacioj. 33, 151-159 (1990).
[3] Ikehata, R., Matsuyama, T.: On global solutions and energy decay for the wave equations of Kirchhoff type with
nonlinear damping terms. Journal of Mathematical Analysis and Applications. 204, 729-753 (1996).
[4] Ono, K.: Global existence, decay, and blow-up of solutions for some mildly degenerate nonlinear Kirchhoff strings.
Journal of Differential Equations. 137, 273-301 (1997).
[5] Taniguchi, T.: Existence and asymptotic behaviour of solutions to weakly damped wave equations of Kirchhoff type with
nonlinear damping and source terms. Journal of Mathematical Analysis and Applications. 361(2), 566-578 (2010).
[6] Han, X., Wang, M.: Global existence and blow-up of solutions for nonlinear viscoelastic wave equation with degenerate
damping and source. Mathematische Nachrichten. 284(5-6), 703-716 (2011).
[7] Pitts, D. R., Rammaha, M. A.: Global existence and nonexistence theorems for nonlinear wave equations. Indiana
University Mathematics Journal. 51(6), 1479-1509 (2002).
[8] Barbu, V., Lasiecka, I., Rammaha, M. A.: Blow-up of generalized solutions to wave equations with nonlinear degenerate
damping and source terms. Indiana University Mathematics Journal. 56(3), 995-1022 (2007).
[9] Barbu, V., Lasiecka, I., Rammaha, M. A.: On nonlinear wave equations with degenerate damping and source terms.
Transactions of the American Mathematical Society. 357(7), 2571-2611 (2005).
[10] Hu, Q., Zhang, H.: Blow up and asymptotic stability of weak solutions to wave equations with nonlinear degenerate
damping and source terms. Electronic Journal of Differential Equations. 2007(76), 1-10 (2007).
[11] Xiao, S., Shubin,W.: A blow-up result with arbitrary positive initial energy for nonlinear wave equations with degenerate
damping terms. Journal of Differential Equations. 32, 181-190 (2019).
[12] Ekinci, F., Pi¸skin, E.: Nonexistence of global solutions for the Timoshenko equation with degenerate damping. Discovering
Mathematics(Menemui Matematik). 43(1), 1-8 (2021).
[13] Pi¸skin, E.: Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source
terms. Open Mathematics. 13, 408-420 (2005).
[14] Pi¸skin, E., Irkıl, N.: Blow up positive initial-energy solutions for the extensible beam equation with nonlinear damping
and source terms. Facta Universitatis, Series: Mathematics and Informatics. 31(3), 645-654 (2016).
[15] Pi¸skin, E., Yüksekkaya, H.: Non-existence of solutions for a Timoshenko equations with weak dissipation. Mathematica
Moravica. 22(2), 1-9 (2018).
[16] Pereira, D. C., Nguyen, H., Raposo, C. A., Maranhao, C. H. M.: On the solutions for an extensible beam equation
with internal damping and source terms. Differential Equations & Applications. 11(3), 367-377 (2019).
[17] Pereira, D. C., Raposo, C. A., Maranhao, C. H. M., Cattai, A. P.: Global existence and uniform decay of solutions
for a Kirchhoff beam equation with nonlinear damping and source term. Differential Equations and Dynamical
Systems.(2021). https://doi.org/10.1007/s12591-021-00563-x
[18] Pi¸skin, E., Ekinci, F.: General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with
degenerate damping terms. Mathematical Methods in the Applied Sciences. 42(16), 1-21 (2019).
[19] Pi¸skin, E., Ekinci, F.: Local existence and blow up of solutions for a coupled viscoelastic Kirchhoff-type equations with
degenerate damping. Miskolc Mathematical Notes. 22(2), 861-874 (2021).
[20] Pi¸skin, E., Ekinci, F.: Blow up of solutions for a coupled Kirchhoff-type equations with degenerate damping terms.
Applications & Applied Mathematics. 14(2), 942-956 (2019).
[21] Pi¸skin, E., Ekinci, F.: Global existence of solutions for a coupled viscoelastic plate equation with degenerate damping
terms. Tbilisi Mathematical Journal. 14, 195-206 (2021).
[22] Pi¸skin, E., Ekinci, F., Zhang, H.: Blow up, lower bounds and exponential growth to a coupled quasilinear wave equations
with degenerate damping terms. Dynamics of Continuous, Discrete and Impulsive Systems. 29, 321-345 (2022).
[23] Ekinci, F., Pi¸skin, E., Boulaaras, S. M., Mekawy, I.: Global existence and general decay of solutions for a quasilinear
system with degenerate damping terms. Journal of function Spaces. 2021, 4316238 (2021).
[24] Ekinci, F., Pi¸skin, E.: Blow up and exponential growth to a Petrovsky equation with degenerate damping. Universal
Journal of Mathematics and Applications. 4(2), 82-87 (2021).
[25] Ekinci, F., Pi¸skin, E.: Global existence and growth of solutions to coupled degeneratly damped Klein-Gordon equations.
Al-Qadisiyah Journal of Pure Science. 27(1), 29-40 (2022).
[26] Ekinci, F., Pi¸skin, E.: Growth of solutions for fourth order viscoelastic system. Sigma Journal of Engineering and
Natural Sciences. 39(5), 41-47 (2021).
[27] Ekinci, F., Pi¸skin, E., Zennir, K.: Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic
Petrovsky equations with degenerate damping terms. Journal of Information and Optimization Sciences. 43(4),
705-733 (2022).
[28] Pi¸skin, E., Ekinci, F.: Blow up, exponential growth of solution for a reaction-diffusion equation with multiple nonlinearities.
Tbilisi Mathematical Journal. 12(4), 61-70 (2019).
[29] Pi¸skin, E., Ekinci, F., Zennir, K.: Local existence and blow-up of solutions for coupled viscoelastic wave equations with
degenerate damping terms. Theoretical and Applied Mechanics. 47(1), 123-154 (2020).
[30] Cordeiro, S. M. S., Pereira, D. C., Ferreira, J., Raposo, C. A.: Global solutions and exponential decay to a Klein–Gordon
equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term. Partial Differential
Equations in Applied Mathematics. 3, 100018 (2021).
Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term
In this paper, we consider a Kirchhoff-type viscoelastic equation with degenerate damping term have initial and Dirichlet boundary conditions. We obtain the blow up and exponential growth of solutions with negative initial energy.
[1] Barbu, V., Lasiecka, I., Rammaha, M. A.: Existence and uniqueness of solutions to wave equations with nonlinear
degenerate damping and source terms. Control Cybernetics. 34(3), 665-687 (2005).
[2] Nishihara, K., Yamada, Y.: On global solutions of some degenerate quasilinear hyperbolic equations with dissipative
terms. Funkcialaj Ekvacioj. 33, 151-159 (1990).
[3] Ikehata, R., Matsuyama, T.: On global solutions and energy decay for the wave equations of Kirchhoff type with
nonlinear damping terms. Journal of Mathematical Analysis and Applications. 204, 729-753 (1996).
[4] Ono, K.: Global existence, decay, and blow-up of solutions for some mildly degenerate nonlinear Kirchhoff strings.
Journal of Differential Equations. 137, 273-301 (1997).
[5] Taniguchi, T.: Existence and asymptotic behaviour of solutions to weakly damped wave equations of Kirchhoff type with
nonlinear damping and source terms. Journal of Mathematical Analysis and Applications. 361(2), 566-578 (2010).
[6] Han, X., Wang, M.: Global existence and blow-up of solutions for nonlinear viscoelastic wave equation with degenerate
damping and source. Mathematische Nachrichten. 284(5-6), 703-716 (2011).
[7] Pitts, D. R., Rammaha, M. A.: Global existence and nonexistence theorems for nonlinear wave equations. Indiana
University Mathematics Journal. 51(6), 1479-1509 (2002).
[8] Barbu, V., Lasiecka, I., Rammaha, M. A.: Blow-up of generalized solutions to wave equations with nonlinear degenerate
damping and source terms. Indiana University Mathematics Journal. 56(3), 995-1022 (2007).
[9] Barbu, V., Lasiecka, I., Rammaha, M. A.: On nonlinear wave equations with degenerate damping and source terms.
Transactions of the American Mathematical Society. 357(7), 2571-2611 (2005).
[10] Hu, Q., Zhang, H.: Blow up and asymptotic stability of weak solutions to wave equations with nonlinear degenerate
damping and source terms. Electronic Journal of Differential Equations. 2007(76), 1-10 (2007).
[11] Xiao, S., Shubin,W.: A blow-up result with arbitrary positive initial energy for nonlinear wave equations with degenerate
damping terms. Journal of Differential Equations. 32, 181-190 (2019).
[12] Ekinci, F., Pi¸skin, E.: Nonexistence of global solutions for the Timoshenko equation with degenerate damping. Discovering
Mathematics(Menemui Matematik). 43(1), 1-8 (2021).
[13] Pi¸skin, E.: Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source
terms. Open Mathematics. 13, 408-420 (2005).
[14] Pi¸skin, E., Irkıl, N.: Blow up positive initial-energy solutions for the extensible beam equation with nonlinear damping
and source terms. Facta Universitatis, Series: Mathematics and Informatics. 31(3), 645-654 (2016).
[15] Pi¸skin, E., Yüksekkaya, H.: Non-existence of solutions for a Timoshenko equations with weak dissipation. Mathematica
Moravica. 22(2), 1-9 (2018).
[16] Pereira, D. C., Nguyen, H., Raposo, C. A., Maranhao, C. H. M.: On the solutions for an extensible beam equation
with internal damping and source terms. Differential Equations & Applications. 11(3), 367-377 (2019).
[17] Pereira, D. C., Raposo, C. A., Maranhao, C. H. M., Cattai, A. P.: Global existence and uniform decay of solutions
for a Kirchhoff beam equation with nonlinear damping and source term. Differential Equations and Dynamical
Systems.(2021). https://doi.org/10.1007/s12591-021-00563-x
[18] Pi¸skin, E., Ekinci, F.: General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with
degenerate damping terms. Mathematical Methods in the Applied Sciences. 42(16), 1-21 (2019).
[19] Pi¸skin, E., Ekinci, F.: Local existence and blow up of solutions for a coupled viscoelastic Kirchhoff-type equations with
degenerate damping. Miskolc Mathematical Notes. 22(2), 861-874 (2021).
[20] Pi¸skin, E., Ekinci, F.: Blow up of solutions for a coupled Kirchhoff-type equations with degenerate damping terms.
Applications & Applied Mathematics. 14(2), 942-956 (2019).
[21] Pi¸skin, E., Ekinci, F.: Global existence of solutions for a coupled viscoelastic plate equation with degenerate damping
terms. Tbilisi Mathematical Journal. 14, 195-206 (2021).
[22] Pi¸skin, E., Ekinci, F., Zhang, H.: Blow up, lower bounds and exponential growth to a coupled quasilinear wave equations
with degenerate damping terms. Dynamics of Continuous, Discrete and Impulsive Systems. 29, 321-345 (2022).
[23] Ekinci, F., Pi¸skin, E., Boulaaras, S. M., Mekawy, I.: Global existence and general decay of solutions for a quasilinear
system with degenerate damping terms. Journal of function Spaces. 2021, 4316238 (2021).
[24] Ekinci, F., Pi¸skin, E.: Blow up and exponential growth to a Petrovsky equation with degenerate damping. Universal
Journal of Mathematics and Applications. 4(2), 82-87 (2021).
[25] Ekinci, F., Pi¸skin, E.: Global existence and growth of solutions to coupled degeneratly damped Klein-Gordon equations.
Al-Qadisiyah Journal of Pure Science. 27(1), 29-40 (2022).
[26] Ekinci, F., Pi¸skin, E.: Growth of solutions for fourth order viscoelastic system. Sigma Journal of Engineering and
Natural Sciences. 39(5), 41-47 (2021).
[27] Ekinci, F., Pi¸skin, E., Zennir, K.: Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic
Petrovsky equations with degenerate damping terms. Journal of Information and Optimization Sciences. 43(4),
705-733 (2022).
[28] Pi¸skin, E., Ekinci, F.: Blow up, exponential growth of solution for a reaction-diffusion equation with multiple nonlinearities.
Tbilisi Mathematical Journal. 12(4), 61-70 (2019).
[29] Pi¸skin, E., Ekinci, F., Zennir, K.: Local existence and blow-up of solutions for coupled viscoelastic wave equations with
degenerate damping terms. Theoretical and Applied Mechanics. 47(1), 123-154 (2020).
[30] Cordeiro, S. M. S., Pereira, D. C., Ferreira, J., Raposo, C. A.: Global solutions and exponential decay to a Klein–Gordon
equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term. Partial Differential
Equations in Applied Mathematics. 3, 100018 (2021).
Ekinci, F., & Pişkin, E. (2023). Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term. Mathematical Sciences and Applications E-Notes, 11(3), 153-163. https://doi.org/10.36753/mathenot.1005570
AMA
Ekinci F, Pişkin E. Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term. Math. Sci. Appl. E-Notes. September 2023;11(3):153-163. doi:10.36753/mathenot.1005570
Chicago
Ekinci, Fatma, and Erhan Pişkin. “Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation With Degenerate Damping Term”. Mathematical Sciences and Applications E-Notes 11, no. 3 (September 2023): 153-63. https://doi.org/10.36753/mathenot.1005570.
EndNote
Ekinci F, Pişkin E (September 1, 2023) Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term. Mathematical Sciences and Applications E-Notes 11 3 153–163.
IEEE
F. Ekinci and E. Pişkin, “Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term”, Math. Sci. Appl. E-Notes, vol. 11, no. 3, pp. 153–163, 2023, doi: 10.36753/mathenot.1005570.
ISNAD
Ekinci, Fatma - Pişkin, Erhan. “Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation With Degenerate Damping Term”. Mathematical Sciences and Applications E-Notes 11/3 (September 2023), 153-163. https://doi.org/10.36753/mathenot.1005570.
JAMA
Ekinci F, Pişkin E. Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term. Math. Sci. Appl. E-Notes. 2023;11:153–163.
MLA
Ekinci, Fatma and Erhan Pişkin. “Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation With Degenerate Damping Term”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 3, 2023, pp. 153-6, doi:10.36753/mathenot.1005570.
Vancouver
Ekinci F, Pişkin E. Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term. Math. Sci. Appl. E-Notes. 2023;11(3):153-6.