Applied and Computational Mathematics
Volume 5, Issue 1, February 2016, Pages: 18-22
Received: Jan. 6, 2016;
Accepted: Jan. 20, 2016;
Published: Feb. 18, 2016
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Haijie Pei, College of Mathematic and Information, China West Norm University, Nanchong, P. R. China
Wenbo Zhao, College of Mathematic and Information, China West Norm University, Nanchong, P. R. China
In this paper, we investigate a diffusion system of two parabolic equations with more general singular coupled boundary fluxes. Within proper conditions, we prove that the finite quenching phenomenon happens to the system. And we also obtain that the quenching is non-simultaneous and the corresponding quenching rate of solutions. This extends the original work by previous authors for a heat system with coupled boundary fluxes subject to non-homogeneous Neumann boundary conditions.
Quenching for a Diffusion System with Coupled Boundary Fluxes, Applied and Computational Mathematics.
Vol. 5, No. 1,
2016, pp. 18-22.
Copyright © 2016 Authors retain the copyright of this article.
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H. Kawarada. On solutions of initial boundary value problem for
, Publ. Res. Inst. Math. Sci. 10(1975), 729-736.
R. Ferreira, A de Pablo, F. Quirs, J. D. Rossi. Non-simultaneous quenching in a system of heat equations coupled at the boundary. Z. Angew. Math. Phys., 57(2006), 586-594.
S. N. Zheng, X. F. Song. Quenching rates for heat equations with coupled nonlinear boundary flux. Sci. China Ser. A. 2008; 51: 1631-1643.
M. Fila, H. A. Levine. Quenching on the boundary. Nonlinear Anal., 21(1993), 795-802.
R. H. Ji, C. Y. Qu, L. D. Wang. Simultaneous and non-simultaneous quenching for coupled parabolic system, Appl. Anal., 94(2), 2015, 233-250.
A. de Pablo, F. Quirós, J. D. Rossi. Non-simultaneous quenching, Appl. Math. Lett. 15 (2002), 265–269.
Y. H. Zhi, C. L. Mu, Non-simultaneous quenching in a semilinear parabolic system with weak singularities of logarithmic type. Applied Mathematics and Computation, 196(2008), 17-23.
R. H. Ji, S. S. Zhou, S. N. Zheng. Quenching behavior of solutions in coupled heat equations with singular multi- nonlinearities, Applied Mathematics and Computation, 223 (2013), 401–410.
C. Y. Chan. Recent advances in quenching phenomena, Proc. Dynam. Systems. Appl. 2(1996), 107-113.
H. A. Levine. The phenomenon of quenching: a survey, in: Trends in the Theory and Practice of NonLinear Analysis, North Holland, New York, 1985, pp. 275-286.
H. A. Levine, J. T. Montgomery. The quenching of solutions of some nonlinear parabolic equations, SIAM J. Math. Anal. 11 (1980), 842-847.
T. Salin. On quenching with logarithmic singularity, Nonlinear Anal. TMA. 52 (2003), 261-289.
C. L. Mu, S. M. Zhou, D. M. Liu. Quenching for a reaction-diffusion system with logarithmic singularity. Nonlinear Anal., 71(2009), 5599-5605.