Profile of blow-up solution to hyperbolic system with nonlocal term

Abstract

This paper is concerned with a nonlocal hyperbolic system as follows: u(tt) = Delta u + (integral(Omega)vdx)(p) for x is an element of R-N, t > 0, u(tt) = Delta v + (integral(Omega)vdx)(q) for x is an element of R-N, t > 0, u(x,0) = u(0)(x), u(t)(x,0) = u(01)(x) for x is an element of R-N, v(x,0) = v(0)(x), v(t)(x,0) = v(01)(x) for x is an element of R-N, where 1 <= N <= 3, p >= 1, q >= 1 and pq > 1. Here the initial values are compactly supported and Omega subset of R-N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed.