[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 5 : Energy Estimates for the Linear Symmetric Hyperbolic System

We derive the corresponding estimates for higher derivatives from the basic energy estimates which was given in the last week. We also prove a simple corollary using this result. And we discuss about the finite propagation speed of the hyperbolic … Continue reading

[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

[M1 Seminar] Week 1 : Introduction to Nonlinear Wave Equations

   For nonlinear wave equations, we cannot guarantee that the solutions exist for some initial value problems. Also the global solutions may exist but also it may have some singularities depending on the initial conditions. Thus we need the global existence … Continue reading