Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
We consider the Cauchy problem for the system of weakly coupled semi-linear damped wave equations
with small initial data. The global existence of the solution has been proved by constructing a
contract mapping in some suitably function space in the supercritical case, which generalizes the results
to the system in dimensional space $n\leq 5$. The proof is based on the estimates of solution operator for the linear damped wave equation.