Non-simultaneous quenching in a semilinear parabolic system with weak singularities of logarithmic type

作者：Zhi Yuanhong^*; Mu Chunlai

来源：Applied Mathematics and Computation, 2008, 196(1): 17-23.

DOI：10.1016/j.amc.2007.05.030

• weak singularity
• quenching
• quenching point
• quenching rate
• semilinear parabolic system

In this paper, we are interested in the possibility of non-simultaneous quenching for positive solutions of a coupled system of two semilinear parabolic equations with weak singularities of logarithmic type, u(1)=u(xx)+log(alpha nu), nu(1)=nu(xx) + log(beta u), 0 < alpha, beta < 1, with homogeneous Neumann boundary conditions and positive initial data. Under some assumptions on the initial data and parameters a, P, we prove that the quenching is always non-simultaneous. We also give the quenching rate when the quenching is non-simultaneous. Finally, we show that our results can be used to a blow-up problem.

• 出版日期2008-2-15
• 单位云南大学; 重庆大学