Asymptotic Analysis Of Solutions To Parabolic System Coupled Via Mixed Type Sources

In this paper, we consider a semi-linear parabolic system u_t = u_xx+e^pvu^α, v_t= v_xx+u^qe^Î’v; in [0,1]×(0,T),with homogeneous Neumann boundary conditions . We find that u(1,t), e^v(1,t)goes to infinity like (T-t)^-k₁, (T -t)^-k₂ respectively, where k₁, k₂ are the solutions ofIn the first chapter, we briefly describes the background of our research questions. In the second chapter, we lists some basic knowledge of parabolic equations associated with this article. In the third chapter, we get a inequality about the solutions of the system, using operator methods. By constructing upper and lower solutions, we prove that the solutions simultaneously Blow-up in finite time, for any non-negative initial value. In the last Chapter, We further simplify the equations as a single equation of the problem issues, using the comparison principle for many times , obtained the Blow-up rate estimates of the solutions.