The Global Existence And Blow-up Solutions For A System Of Nonlocal Wave Equations

In this paper, we mainly deal with two global existence and blow-up solutions for systems of nonlocal wave equations with different conditions. Firstly, we consider the initial value problem for a system of nonlocal wave equations: where and i=1,2,3. All of the initial values are continuous and i=1,2,3. By symmetry, we assume p₁ ≤ p₂ ≤ p₃. In this paper we prove the solutions of (1) is global existence with the condition 0 < p₂ p₃≤ 1; While the solutions of (1) is blowing-up with the condition p1 ≥ 1, p₁ p₂ p₃> 1. And we present the growth rates of (1) at blow-up. Second, we study the initial boundary values for a system of nonlocal wave equations with semi-infinte field condition: i=1,2. All of the values are continuous and By symmetry, we assume p ≤ q. In this paper we prove the solutions of (2) is global existence with the condition 0 < pq≤ 1; And we presume . By this assumption, we prove the solutions (2) is blowing-up when the system of (2) has the condition...