[M1 Seminar II] Week 5 : High Energy Estimates

We prove the high energy estimates for the nonlinear wave equation on the nonlinearity $\alpha =1$. In fact, this problem is a special case of the quasi-linear symmetric hyperbolic system with some assumptions. By the help of the previous existence … Continue reading

[M1 Seminar] Week 6,7 : A Global Existence Theorem to the Linear Symmetric Hyperbolic Systems

This week, we prove the global existence theorem to the linear symmetric hyperbolic system by using the standard energy inequality. M1_Semi_Week6-7  

[M1 Seminar] Week 2 : Decay Estimates for Linear Wave Equations

   This week, we have considered only odd space dimensions for the linear wave equation to prove two estimates in Theorem 2.1. The proof was done for the simple case. For the general cases including the case of even dimensions, we … Continue reading