The Critical Exponent Of A Parabolic System With Logarithmic Nonlinearities

In this paper, we study the critical exponent of a parabolic system with logarithmic nonlinearities of where p, q,α,β> 0.We obtain that the solutions are global if 2q < max(l,α) and 2p < max(l,β), and blow up if 2q > max(l,α) or 2p > max(l,β). If 2q = max(l,α) or 2p = max(l,β), global existence or non-existence of solutions is determined by the coefficientsλ₁ andλ₂.In the introduction, we give the background to the parabolic system with logarithmic nonlinearities. In section 2, we give some basic knowledge to be used in this paper. In section 3, we describe the main results of the paper, and then prove the theorems in section 4. In the last section, we discuss all the conclusions obtained in this paper.