Blowup, Global Fast and Slow Solutions for a Semilinear Combustible System

Abstract

" In this paper, we investigate a semilinear combustible system $u_t-du_{xx}=v^p, v_t-dv_{xx}=u^q$ with double fronts free boundary, where p \u2265 1, q \u2265 1. For such a problem, we use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup and global existence property of the solution. Our results show that when pq \u203a 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p \u203a 1, q \u203a 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small."