Exponential growth of solutions for a parabolic system

Abstract

In this paper, we investigated the initial boundary problem of a class of doubly nonlinear parabolic systems. We prove exponential growth of solution with negative initial energy.

Keywords

• Exponential growth

References

1. 1. Pang J, Qiao B. Blow-up of solution for initial boundary value problem of reaction diffusion equations. Journal of Advances in Mathematics 2015;10(1):3138-3144.
2. 2.Bebernes J, Eberly D. Mathematical Problems from Combustion Theory. Applied Mathematical Science. Springer-Verlag: Berlin; 1989.
3. 3. Pao CV. Nonlinear Parabolic and Elliptic Equations. Plenum, New York; 1992.
4. 4. Escerh J, Yin Z. Stable equilibra to parabolic systems in unbounded domains. Journal of Nonlinear Mathematical Physics 2004;11(2):243-255.
5. 5. Zhou H. Blow-up rates for semilinear reaction-diffusion systems. Journal of Differential Equations 2014;257 :843-867.
6. 6. Escher J, Yin Z. On the stability of equilibria to weakly coupled parabolic systems in unbounded domains. Nonlinear Analysis 2005;60:1065-1084.
7. 7. Escobedo M, Herrero MA. A semilinear reaction diffusion system in a bounded domain. Annali di Matematica Pura ed Applicata 1993;165:315–336.
8. 8. Escobedo M, Levine HA. Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations. Archive for Rational Mechanics and Analysis 1995;129:47-100.

9. 9. Alaa N. Global existence for reaction-diffusion systems with mass control and critical growth with respect to the gradient. Journal of Mathematical Analysis and Applications 2001;253:532-557.
10. 10. Wang RN, Tang ZW. Global existence and asymptotic stability of equilibria to reaction-diffusion systems. Journal of Physics A: Mathematical and Theoretical 2009;42, Article ID 235205.
11. 11. Yadav OP, Jiwari R. A finite element approach for analysis and computational modelling of coupled reaction diffusion models. Numerical Methods for Partial Differential Equations 2018;1-21.