Abstract
AbstractIn this paper, we establish the Fujita type theorem for a homogeneous Neumann outer problem of the coupled quasilinear convection–diffusion equations and formulate the critical Fujita exponent. Besides, the influence of diffusion term, reaction term, and convection term on the global existence and the blow-up property of the problem is revealed. Finally, we discuss the large time behavior of the solution to the outer problem in the critical case and describe the asymptotic behavior of the solution.
Funder
National Natural Science Foundation of China
Department of Science and Technology of Jilin Province
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference31 articles.
1. Aguirre, J., Escobedo, M.: On the blow-up of solutions of a convective reaction diffusion equation. Proc. R. Soc. Edinb., Sect. A 123(3), 433–460 (1993)
2. Deng, K., Levine, H.: The role of critical exponents in blow-up theorems: the sequel. J. Math. Anal. Appl. 243, 85–126 (2000)
3. Díaz, J.I., Hernández, J., Ilyasov, Y.Sh.: On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets. Adv. Nonlinear Anal. 9(1), 1046–1065 (2020)
4. Escobedo, M., Herrero, M.: Boundedness and blow up for a semilinear reaction–diffusion system. J. Differ. Equ. 89, 176–202 (1991)
5. Fujita, H.: On the blowing up of solutions of the Cauchy problem for $u_{t}=\Delta u+u^{1+\alpha }$. J. Fac. Sci., Univ. Tokyo, Sect. I 13, 109–124 (1966)