Blow up of solutions for a parabolic equation of Kirchhoff-type with multiple nonlinearities

Year 2020, Volume: 4 Issue: 1, 10 - 13, 30.12.2020

Erhan Pişkin Fatma Ekinci

Abstract

In this paper, we investigated a class of doubly nonlinear parabolic systems with Krichhoff-type.
We prove a blow up of solutions with negatif initial energy.

Keywords

Blow up

References

• Han Y, Li Q. Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy. Computers and Mathematics with Applications 2018; 75: 3283-3297.
• Han Y, Gao W, Sun Z, Li H. Upper and lower bounds of blow-up time to a parabolic type Kirchhoff equation with arbitrary initial energy. Computers and Mathematics with Applications 2018; 76: 2477-2483.
• Tuan NH, Nam DHQ, Vo TMN. On a backward problem for the Kirchhoff’s model of parabolic type. Computers and Mathematics with Applications 2019; 77: 115-33.
• Dawidowski L. The quasilinear parabolic kirchhoff equation. Open Mathematics 2017;15 :382.392.
• Gobbino M. Quasilinear degenerate parabolic equations of Kirchhoff type. Mathematical Methods and Applied Science 1999; 22(5): 375-388.
• Kundu S, Pani AK, Khebchareon M. On Kirchhoff’s model of parabolic type. Numerical Functional Analysis and Optimization, 2016; 37(6): 719-752.
• Chang N, Chipot M. Nonlinear nonlocal evolution problems. RACSAM, Rev. R. Acad. Cien. Ser.A. Mat. 2003; 97: 393-415.
• Zheng S, Chipot M. Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms. Asymptotic Analysis 2005; 45: 301-312.
• Korpusov MO, Sveshnikov AG. Sufficent close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq equation, Computational Mathematics and Mathematical Physics 2008; 48(9): 1591-1599.