Global solutions and self-similar solutions of the coupled system of semilinear wave equations in three space dimensions
The authors treat the coupled system of wave equations \(u_{tt}-\triangle u=|u|^{p_1}|v|^{q_1}\), \(v_{tt}-\triangle v=|u|^{p_2}|v|^{q_2}\), \(x\in \mathbb{R}^n\), \(t>0.\) They give the lower bounds of \(p_j\), \(q_j\) to assure the global existence of a class of solutions including self-similar solutions for small initial data. If such conditions on \(p_j\), \(q_j\) are not satisfied, then no self-similar solution exists even for small data.
scientific article; zbMATH DE number 1890749