[1] Y. Han, Q. Li, Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and
Mathematics with Applications, 75, (2018), 3283-3297.
[2] Y. Han, W. Gao, Z. Sun, H. Li, Upper and lower bounds of blow-up time to a parabolic type Kirchhoff equation with arbitrary initial energy, Computers
and Mathematics with Applications, 76, (2018), 2477-2483.
[3] N. H. Tuan, D. H. Q. Nam, T. M. N. Vo, On a backward problem for the Kirchhoff’s model of parabolic type, Computers and Mathematics with
Applications, 77, (2019), 115-33.
[4] L. Dawidowski, The quasilinear parabolic Kirchhoff equation, Open Mathematics, 15, (2017), 382–392.
[5] M. Gobbino, Quasilinear degenerate parabolic equations of Kirchhoff type, Mathematical Methods in the Applied Science, 22(5), (1999), 375–388.
[6] S. Kundu, K. A. Pani, M. Khebchareon, On Kirchhoff’s model of parabolic type, Numerical Functional Analysis and Optimization, 37(6), (2016),
719–752.
[7] N. H. Chang, M. Chipot, Nonlinear nonlocal evolution problems, RACSAM, Rev. R. Acad. Cien. Ser. A. Mat., 97, (2003), 393–415.
[8] S. Zheng, M. Chipot, Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms, Asymptotic Analysis, 45, (2005), 301–312.
[9] Y. Ye, Global existence and energy decay for a coupled system of Kirchhoff type equations with damping and source terms, Acta Mathematicae
Applicatae Sinica, 32(3), (2016), 731-738.
[10] K. Narasimha, Nonlinear vibration of an elastic string, Journal of Sound and Vibration, 8, (1968), 134–146.
[11] E. Pişkin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate dampings terms, Journal of Nonlinear
Functional Analysis, 2018, (2018), 1-14.
[12] K. Ono, Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings, Journal of Differential Equations,
137, (1997), 273-301.
[13] B. Cheng, X. Wu, Existence results of positive solutions of Kirchhoff type problems, Nonlinear Analysis, 71, (2009), 4883-4892.
[14] Y. Zhijian, Longtime behavior of the Kirchhoff type equation with strong damping on Rn, Journal of Differential Equations, 242, (2007), 269-286.
[15] M. O. Korpusov, A. G. Sveshnikov, Sufficent close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq
equation, Computational Mathematics and Mathematical Physics, 48(9), (2008), 1591-1599.
[16] O. Ladyzenskaia, V. Solonikov, N. Uraltceva, Linear and quasilinear parabolic equations of second order, Translation of Mathematical Monographs.
AMS, Rhode Island, 1968.
Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities
In this paper, we investigate a class of doubly nonlinear parabolic systems with Krichhoff-type. We prove a nonexistence of global solutions and exponential growth of solution with negative initial energy.
[1] Y. Han, Q. Li, Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and
Mathematics with Applications, 75, (2018), 3283-3297.
[2] Y. Han, W. Gao, Z. Sun, H. Li, Upper and lower bounds of blow-up time to a parabolic type Kirchhoff equation with arbitrary initial energy, Computers
and Mathematics with Applications, 76, (2018), 2477-2483.
[3] N. H. Tuan, D. H. Q. Nam, T. M. N. Vo, On a backward problem for the Kirchhoff’s model of parabolic type, Computers and Mathematics with
Applications, 77, (2019), 115-33.
[4] L. Dawidowski, The quasilinear parabolic Kirchhoff equation, Open Mathematics, 15, (2017), 382–392.
[5] M. Gobbino, Quasilinear degenerate parabolic equations of Kirchhoff type, Mathematical Methods in the Applied Science, 22(5), (1999), 375–388.
[6] S. Kundu, K. A. Pani, M. Khebchareon, On Kirchhoff’s model of parabolic type, Numerical Functional Analysis and Optimization, 37(6), (2016),
719–752.
[7] N. H. Chang, M. Chipot, Nonlinear nonlocal evolution problems, RACSAM, Rev. R. Acad. Cien. Ser. A. Mat., 97, (2003), 393–415.
[8] S. Zheng, M. Chipot, Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms, Asymptotic Analysis, 45, (2005), 301–312.
[9] Y. Ye, Global existence and energy decay for a coupled system of Kirchhoff type equations with damping and source terms, Acta Mathematicae
Applicatae Sinica, 32(3), (2016), 731-738.
[10] K. Narasimha, Nonlinear vibration of an elastic string, Journal of Sound and Vibration, 8, (1968), 134–146.
[11] E. Pişkin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate dampings terms, Journal of Nonlinear
Functional Analysis, 2018, (2018), 1-14.
[12] K. Ono, Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings, Journal of Differential Equations,
137, (1997), 273-301.
[13] B. Cheng, X. Wu, Existence results of positive solutions of Kirchhoff type problems, Nonlinear Analysis, 71, (2009), 4883-4892.
[14] Y. Zhijian, Longtime behavior of the Kirchhoff type equation with strong damping on Rn, Journal of Differential Equations, 242, (2007), 269-286.
[15] M. O. Korpusov, A. G. Sveshnikov, Sufficent close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq
equation, Computational Mathematics and Mathematical Physics, 48(9), (2008), 1591-1599.
[16] O. Ladyzenskaia, V. Solonikov, N. Uraltceva, Linear and quasilinear parabolic equations of second order, Translation of Mathematical Monographs.
AMS, Rhode Island, 1968.
Pişkin, E., & Ekinci, F. (2020). Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp Journal of Mathematics, 8(1), 216-222.
AMA
Pişkin E, Ekinci F. Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp J. Math. Nisan 2020;8(1):216-222.
Chicago
Pişkin, Erhan, ve Fatma Ekinci. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics 8, sy. 1 (Nisan 2020): 216-22.
EndNote
Pişkin E, Ekinci F (01 Nisan 2020) Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp Journal of Mathematics 8 1 216–222.
IEEE
E. Pişkin ve F. Ekinci, “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities”, Konuralp J. Math., c. 8, sy. 1, ss. 216–222, 2020.
ISNAD
Pişkin, Erhan - Ekinci, Fatma. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics 8/1 (Nisan 2020), 216-222.
JAMA
Pişkin E, Ekinci F. Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp J. Math. 2020;8:216–222.
MLA
Pişkin, Erhan ve Fatma Ekinci. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics, c. 8, sy. 1, 2020, ss. 216-22.
Vancouver
Pişkin E, Ekinci F. Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp J. Math. 2020;8(1):216-22.